van der Waals Metallic Transition Metal Dichalcogenides - Chemical

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Cite This: Chem. Rev. 2018, 118, 6297−6336

van der Waals Metallic Transition Metal Dichalcogenides Gang Hee Han,†,‡,∥ Dinh Loc Duong,†,‡,∥ Dong Hoon Keum,†,‡ Seok Joon Yun,†,‡ and Young Hee Lee*,†,‡,§ †

Center for Integrated Nanostructure Physics (CINAP), Institute for Basic Science (IBS), Suwon 16419, Republic of Korea Department of Energy Science, Sungkyunkwan University, Suwon 16419, Republic of Korea § Department of Physics, Sungkyunkwan University, Suwon 16419, Republic of Korea

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‡

ABSTRACT: Transition metal dichalcogenides are layered materials which are composed of transition metals and chalcogens of the group VIA in a 1:2 ratio. These layered materials have been extensively investigated over synthesis and optical and electrical properties for several decades. It can be insulators, semiconductors, or metals revealing all types of condensed matter properties from a magnetic lattice distorted to superconducting characteristics. Some of these also feature the topological manner. Instead of covering the semiconducting properties of transition metal dichalcogenides, which have been extensively revisited and reviewed elsewhere, here we present the structures of metallic transition metal dichalcogenides and their synthetic approaches for not only high-quality wafer-scale samples using conventional methods (e.g., chemical vapor transport, chemical vapor deposition) but also local small areas by a modification of the materials using Li intercalation, electron beam irradiation, light illumination, pressures, and strains. Some representative band structures of metallic transition metal dichalcogenides and their strong layer-dependence are reviewed and updated, both in theoretical calculations and experiments. In addition, we discuss the physical properties of metallic transition metal dichalcogenides such as periodic lattice distortion, magnetoresistance, superconductivity, topological insulator, and Weyl semimetal. Approaches to overcome current challenges related to these materials are also proposed.

CONTENTS 1. Introduction 2. Crystal Structures of Layered Transition Metal Dichalcogenides 2.1. Structural Classifications 2.1.1. H and T Phases 2.1.2. Extended Structures 2.2. Other Layered Transition Metal Dichalcogenides and Related Compounds 2.3. Table of Metallic Layered Transition Metal Dichalcogenides Structures 3. Synthesis 3.1. Bulk Single Crystal Growth 3.1.1. Flux Method 3.1.2. Chemical Vapor Transport 3.2. Chemical Vapor Deposition 3.3. Other Synthetic Methods 3.3.1. Molecular Beam Epitaxy 3.3.2. Li-Intercalation 3.3.3. Phase Transition by Laser and e-Beam Irradiation 4. Electronic Structures 4.1. Electronic Structures of Representative Metallic Layered Transition Metal Dichalcogenides 4.1.1. 1T-TiS2 and 1T-TiSe2 4.1.2. 1T-VSe2 4.1.3. 1T- and 2H-NbSe2 © 2018 American Chemical Society

4.1.4. 1T-, 2H-, and 4H-TaS2 4.2. Layer Dependence of the Band Structure in Metallic Layered Transition Metal Dichalcogenides 5. Periodic Lattice Distortion or Charge Density Wave in Matallic Layered Transition Metal Dichalcogenides 5.1. Periodic Lattice Distortion Phenomenon 5.2. Mechanism for Periodic Lattice Distortion Transition 5.3. Experimental Characterization of Periodic Lattice Distortion 5.4. Tuning Periodic Lattice Distortion Transition and Superconductivity Phase Formation 6. Other Properties 6.1. Magnetism in 2D Metallic Layered Transition Metal Dichalcogenides 6.1.1. Magnetism in 2D Materials and Magnetic Metallic Layered Transition Metal Dichalcogenides 6.1.2. Ferromagnetism in Atomically Thin 2D Metallic Layered Transition Metal Dichalcogenides (VS2 and VSe2)

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Special Issue: 2D Materials Chemistry Received: October 15, 2017 Published: June 29, 2018 6297

DOI: 10.1021/acs.chemrev.7b00618 Chem. Rev. 2018, 118, 6297−6336

Chemical Reviews 6.1.3. Strain Effect on Magnetism of Metallic Layered Transition Metal Dichalcogenides 6.1.4. Doping Effect on Magnetism of Metallic Layered Transition Metal Dichalcogenides by Vacancy, Hydrogenation, and Substitution by Dopants 6.2. Weyl Semimetal in 1Td WTe2 and MoTe2 7. Summary and Perspectives Author Information Corresponding Author ORCID Author Contributions Notes Biographies Acknowledgments Abbreviations Used References

Review

area. Weyl semimetals and phase engineering associated with contact resistance are examples of newly adopted research area in m-LTMdCs.8−10 In the synthetic point of view, some advances have been made through chemical vapor deposition method (CVD). Monolayer LTMdCs are easily accessible by CVD, which is rather difficult to obtain by other platforms such as CVT or flux methods. Recent studies on m-LTMdCs have not been conducted much compared to the semiconducting components. Many physical and chemical phenomena are still being studied in m-LTMdCs. This review consists of seven sections including the Introduction. In the next section, we introduce the basic H and T structures of LTMdCs and their extended structures by considering stacking sequences. We also briefly introduce the metal chalcogenides which has different stoichiometric ratios such as 1:1 or 2:3 or ternary (quaternary). However, the properties of those materials are out of scope and excluded in this thematic review. We provide them in the form of a table at the end of the section. In section 3, we introduce various synthesis methods. A brief description of the flux and the CVT methods for the bulk materials are discussed. In particular, section 3.2 summarizes the conventional CVD approaches, which have been developed typically for the synthesis of sLTMdC to date. The process can be extended for the growth of m-LTMdCs. We also briefly introduce the molecular-beam epitaxy method (MBE) and the phase transition of s-LTMdCs to m-LTMdCs through intercalation, laser, or e-beam irradiation in the last section of section 3. It is important to understand the electronic band structure of materials. Combined with the theoretical calculation and the angle-resolved photoemission spectroscopy (ARPES), the band structure of materials are now more clearly visible.11,12 Section 4 discusses the band structure of m-LTMdCs. We provide the electronic structures of transition metals and chalcogens and compare the band structures of representative m-LTMdCs such as TiS2, TiSe2, and VSe2 with theoretical calculations and experimental works determined from ARPES. We further introduce the electronic band structures of the bulk NbSe2 and TaS2, which have both H and T phases. Layer dependence will be discussed in the last part of section 4. The density functional theory (DFT) is the most versatile and common approach for band structure calculations.13,14 The main idea of the DFT is to replace the wave function basic set by the electron charge density, which is called the mean field approximation.15 By this methodology, the huge number of electrons can be treated as the electron density, which is a three-dimensional space function with three degrees of freedom. However, this approach gives rise to difficulties in estimating the exchange (e.g., the interaction originated from the indistinguishable nature of electrons) and correlation (e.g., the energy error when treating electron clouds as an independent object) of electrons. It is the motivation for the development of varieties of different exchange-correlation functions from the local density approximation, generalized gradient approximation to hybrid functionals.16−18 In this section, the band structure using different functionals for one material will be also presented. The appearance of the PLD phases accompanying the superconductivity transition occurs in many m-LTMdCs, which makes this class of layered materials attractive to condensed matter physicists. This issue is the main focus of section 5. The phenomenon of the PLD transitions and their mechanism are described by the intuitive picture of one-

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1. INTRODUCTION Two-dimensional (2D) van der Waals (vdW) layered materials, which have a strong covalent bonding within the layer and weak vdW interaction between the layers, reveal themselves as having unique layer-dependent features distinct from bulk materials. For example, graphene is one of the intensively studied species1 due to their remarkable electrical and optical properties since 2004. In addition, many of layered materials have been discovered for a decade. Boron nitride has been considered as a template to improve the carrier mobility of graphene compared to conventional insulator substrates such as SiO2.2 Other 2D materials, such as black phosphorus,3 borophene,4 silicene,5 and stanene,6 also join the 2D family. In addition, there are numerous compounds consisting of transition metals and chalcogens to form a large category of layered transition metal dichalcogenides (LTMdCs). Revisiting of the first LTMdCs has been made from the semiconducting species such as MoS2, which has long been known as lubricant similar to graphene. Intriguing physical properties of a number of semiconducting LTMdCs (s-LTMdCs) species have already been discussed elsewhere.7 Unlike s-LTMdCs, metallic LTMdCs (m-LTMdCs) (Figure 1) have a finite density of states at the Fermi level and their research fields rather differ from semiconducting materials. Therefore, it is worth revisiting some research topics that are well-known in 3D materials such as charge density wave (CDW) or periodic lattice distortion (PLD), superconductivity, magnetism in metallic 2D vdW materials. Recent progresses in m-LTMdCs has further expanded the research

Figure 1. Types of metals involved in layered dichalcogenides. Blue color indicates transition metals for currently developed metalliclayered dichalcogenides (m-LTMdCs), and yellow, green, and red small rectangles are S, Se, and Te compounds. White rectangles for chalcogen are unreported or nonexist phase in m-LTMdCs. 6298


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Figure 2. Two primary phases for 1:2 (metal:chalcogen) ratio LTMdCs: (a) H phase, (b) T phase.

Because H and T phases do not guarantee the material property as semiconducting and metallic, respectively, we cover both main structures of LTMdCs. However, in this thematic review, we limit our discussion to the physical property of metallic one, which have not been intensively studied as much as semiconducting LTMdCs but potentially have many intriguing physical and chemical properties.7,20−22 2.1.1. H and T Phases. LTMdCs, either semiconducting or metallic phase, consist of two tetrahedrons (Figure 2). Each blue tetrahedron describes the framework of the H and T phases with ball-and-stick models; blue and yellow atoms indicate transition metals and chalcogens, respectively. The lower and upper tetrahedrons are arranged symmetrically from the metal surface (center) to form a trigonal prismatic structure (H-phase) (Figure 2a). Another primary unit, an octahedral or T phase, shown in Figure 2b, is constructed by rotating the upper (or lower) tetrahedron by 180°. The top view of H phase (Figure 2a, inset) shows a hexagonal structure similar to hexagonal boron nitride (h-BN) from the top view. However, in reality, two identical chalcogen layers are divided up and down with respect to the metal layer. In the T phase, chalcogen atoms in the top layer are projected among chalcogen atoms in the bottom layer. (Figure 2b, inset) 2.1.2. Extended Structures. Stacking sequence affects prominent physical properties of the materials such as electronic band structures,23 phonon vibrations,24 and optical properties. 25,26 The numbers appearing in the phase nomenclature such as “2”H, “1”T, “3”R, and “4”H indicates the stacking sequence of LTMdCs. For example, 2H-MoS2 indicates the grouping of two layers with AB-stacking, while 3R-NbS2 describes the repeating of three layers as one group, ABC stacking. Top and side views of the extended structures are shown in Figure 3. The 2H structure is involved in the hexagonal group (group name: P63/mmc); the top view shows a hexagonal lattice by alternating two chalcogen atoms and one transition metal atom. While the majority of 2H structures in LTMdCs exhibit semiconducting properties, very few 2H phases are known to be m-LTMdCs including 2H-NbS2, 2HNbSe2, 2H-TaS2, and 2H-TaSe2.27−30 The 1T phase is the primary structure which belongs to the hexagonal group (P3̅m1) in m-LTMdCs. The structure formed is an octahedron rather than a trigonal prismatic due to the rotation of one tetrahedron. We discuss the material properties in other sections. Dimerization of transition metal atoms induces the distortion of the 1T structure to form the 1T′ phase (P21/ m). In particular, dimerization of the metal atoms induces displacement of chalcogen atoms in an out-of-plane direction

dimensional Peierls distortion. It is worth noting that the PLD transition introduces a lower symmetry structure, which breaks the degeneracy of the electronic band of the normal phase. This is similar to the Jahn−Teller effect in chemistry, where molecules have a tendency to distort their structure to lower symmetry. As a consequence, one energy level will split to form many states, where electrons can occupy a lower energy configuration compared to the one of higher symmetry structures. In contrast, the Peierls model only considers one band model without any degeneracy. We will discuss how to extend the Peierls model to the PLD transition in real materials. We will clarify that it is not necessary to fully open a band gap to maintain the low energy state of the PLD phase. The phonon softening phenomenon and its relation to superconductivity, which always occurs with the PLD transition, will be reviewed. The correlation with the Kohn anomaly, which also reveals the phonon softening due to the change of the electron screening, is also examined. We will also discuss characterization methods for determining the PLD phase transformation. Recently, the emergence of topological matters and 2D ferromagnetism brings attentions to m-LTMdCs, which is discussed in section 6. In detail, we introduce the ferromagnetism in VS2 and VSe2 and discuss the effect of strain, doping, and defects on the magnetic properties. In particular, we will briefly discuss the concept and band structure of Weyl semimetals, which is emerging in the 1T phase MoTe2 and Td phase WTe2 and their alloy formation. The last section summarizes issues and perspectives of synthesis, phase transition, devices, and physical properties. The possibility of phase transition through the alloy and the remaining issues on superconductivity and Weyl semimetals will be also discussed.

2. CRYSTAL STRUCTURES OF LAYERED TRANSITION METAL DICHALCOGENIDES 2.1. Structural Classifications

Chalcogen elements are highly reactive to metals, creating a number of metal chalcogenide combinations with various stoichiometric ratios. Among these compounds, LTMdCs have layered structures with a 1:2 ratio between the metals and chalcogens.19 The unit structure of the LTMdCs includes a transition metal layer sandwiched between two layers of chalcogen atoms. Metal-chalcogen atoms form strong covalent bonds within the layer. Each layer is stacked vertically by a weak vdW interactions, and the layered bulk can typically be exfoliated into individual layers. In the following sections, we introduce the basic structure of H and T phases of LTMdCs. 6299


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Figure 3. Various phases and stacking sequences in LTMdCs.

between 1T and Td is the c-axis angle (α ≠ 90, β = 90), as indicated in Figure 3. The 3R-phase (R3m) includes three layers in the unit cell. For example, NbS2, NbSe2, TaS2, and

and a symmetry transformation from 3- to 2-fold. 1T′-MoTe2 is a representative material in m-LTMdCs.8 The Td structure, found in WTe2,31 is similar to the 1T′ structure. The difference 6300


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Figure 4. Other types of LTMdCs and metal-chalcogen compounds. (a) Ternary or quarternary structures for metal or chalcogen exchange without structural transformations. (b) Layered ternary structure with other compounds such as MnPS3. (c) 1:1 ratio layered metal chalcogenide. (d) Quintuple layered compounds such as Bi2Se3 and Bi2Te3.

common metal chalcogenides, this review covers only a 1:2 ratio layered TMDLTMdCs.

TaSe2, which appear in both H and T phases, also have 3R phases.27−30,32 Two different stacking orders exist in the 4H phase. The 4H structure in Figure 3 is the 4Hb type, which can be described as an alternating phase of T−H−T−H layers, while the unit cell of the 4Ha structure is composed of only H phase layers.33−41

2.3. Table of Metallic Layered Transition Metal Dichalcogenides Structures

A list of m-LTMdCs is provided in Table 1. The first and second columns show types of transition metals and chalcogens, respectively. The metal column includes transition metal species such as Ti, V, Ni, Zr, Nb, Pd, Hf, Ta, Ir, Pt, Mo, and W, which combined with chalcogens such as S, Se, and Te. (See the refs. 8 ,11, 12, 31, 41, 42, 44, 45, 52−138 in the table.) The semiconducting components (s-LTMdCs) such as 2H phase WSe2 and MoSe2 are not included in this table. The third column describes the corresponding phases for each metal-chalcogen combination. H, T, and R are the acronyms of hexagonal, tetragonal, and rhombohedral structures, respectively. In the table, we categorize the synthetic approach as bulk crystal growth, thin film deposition, and monolayer growth of LTMdCs. To avoid confusion, we define the thin film as “the film has several to hundreds layers that exhibits bulk properties”.

2.2. Other Layered Transition Metal Dichalcogenides and Related Compounds

In addition to the typical stoichiometry of 1:2 ratio mLTMdCs, there are other types of transition metal chalcogenides and compounds. Figure 4a shows a typical T phase m-LTMdC structure, for example, that of TiS2 and VS2 or their selenide compounds. Each pure material exhibits metallic behavior.42,43 Figure 4a depicts alloy formation of TiS2 and VS2 to form TixV1−xS2 and TixV1−xSe2, or TiSxSe1−x or VSxSe1−x which maintain a 1:2 metal:chalcogen ratio while the topology does not change by alloying.44,45 This atomic exchanges, whether it is called alloying or doping, could induce its modulation on electrical and phononic properties. Figure 4b shows the structure of the transition metal phosphorus trichalcogenides (C12/m1, monoclinic) or phosphochalcogenides, typically abbreviated as MPX3 (M, metal; P, phosphorus; X, chalcogens), which is a new class of layered materials for spintronics.46,47 Figure 4c shows a material with 1:1 stoichiometry between metal and chalcogen atoms. For example, FeSe has a tetragonal structure (P4/nmm).48 From the Fe plane, chalcogen atoms are alternately positioned in a z-direction. Fe sites can be replaced or doped by Cu atoms. These materials have intriguing physical properties such as high-temperature superconducting above 100 K on the strontium titanate (SrTiO3) substrate.49 Metal chalcogenides which have 2(metal):3(chalcogen) forms a quintuple layer. Bi2Se3, Bi2Te3, and Sb2Te3 are representative materials for this quintuple layer arrangement and well-known as good thermoelectric materials. These materials also reveal characteristics of topological insulators.50,51 Since there are numerous combinations of

3. SYNTHESIS In this section, we discuss several synthetic approaches for mLTMdCs. We have categorized the sections into (i) bulk growth, (ii) film growth including both few layers and monolayer flakes, and (iii) other synthetic methods. The bulk growth section includes flux and CVT methods. Followed section introduces the CVD process which is a representative approach for the materials growth as film formation. With MBE and several other approaches, we also briefly introduce the phase changes by post-treatments such as Li intercalation, laser, and e-beam irradiation in the last section of this chapter. 3.1. Bulk Single Crystal Growth

3.1.1. Flux Method. The flux method is one of the traditional methods which provides a high-quality single crystal in bulk form. To form a crystal, raw materials are liquefied in a solvent flux at high temperature (Figure 5a). The process requires the type of crucible that does not react with the 6301


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Te

S Te

Mo

W

S Se Te

Pt

Td, T′

T (mix) Td, T′

T T T

T

H, T, R H, T, R T′

T

T

H,T, R H,T, R T

T T

T T T

T T T

phase

86 86 86

101

85, 86

76 82

annealing

131, 132

8, 12, 115

102 102 102

flux

31, 133

11, 116, 117, 118

103

91, 92, 93 97, 98 100

88, 89

72 77, 78 83, 84

52, 67 41, 42, 67

61,62 66

44, 45, 52 45, 52, 55 45,52

CVT

87 (B.T)

42

63

others

108, 109, 110, 111, 112, 113, 114

single and poly crystal

119, 120, 121 122, 123, 124

104, 105

94, 95

73, 74, 75 79

68

60 64

53, 54 56

CVD

synthesis approaches film

134

106

99

90

57

MBE

135

71

others

127, 136

125, 126, 127

69, 70

CVD

137, 138

128, 129, 130

106

80,81

58,59

MBE

monolayer

107

96

65

others

The first and second columns are the types of transition metals and chalcogens, respectively. Only metallic components are shown, semiconducting (insulating) components are not included. Each number in the table is a reference number. For 1T-MoS2, refs 108−111 and 113 are monolayer and 112 is few layers samples. Reference 114 includes both mono and few layers experimental data.

a

Te

Te

Pd

Ir

S Se Te

Nb

S Se Te

S Se

Zr

Ta

S Se Te

V

Te

S Se Te

Ti

Hf

chalcogens

metals

Table 1. Table for m-LTMdCs and Their Synthesis Methodsa

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Figure 5. Illustrations of the (a) flux method and (b) chemical vapor transport (CVT) method. (c) 1T′-MoTe2 crystal by flux method. Reproduced with permission from ref 115. Copyright 2016 American Physical Society. (d) WTe2 crystal from flux method. Reprinted with permission from ref 31. Copyright 2014 Macmillan Publishers Ltd.

transport agents are typically pure halogen elements or their compounds, which react easily with the raw materials. Then, the reactants are converted into forms which can be easily vaporized to facilitate transportation. Therefore, the transport agent should be carefully selected. By reacting metals (M:Ti, V, Ni, Zr, Nb, Pd, Sn, Hf, Ta, Ir, Pt, Mo, W) and chalcogens (X:S, Se, Te) with a selected transport agent, MX2 structures can be created in various combinations. The total transport process in the ampule is governed by the chemical equation shown below:

reactants and tolerates high-temperature treatments. In addition, a flux material should have a low melting point so that it can surround the source materials as liquid form and a high boiling point to avoid vaporization during reaction. Moreover, it should be easy to remove the flux after synthesis. NaCl, Sn, and Te fulfill all mentioned requirements and are typically adopted as the flux materials, as shown in Table 2. Table 2. Growth conditions of MoTe2 and WTe2 in the Flux Method

MA(g) + 2X(g) → MX 2(s) + A 2(g)

flux conditions metals

chalcogens

ref

temperature (°C)

flux

Mo

Te

8 12, 115

1000 1000

NaCl Te

W

Te

131 132

825 1000

Te Te

where A is the transport agent. Typically, halogen elements such as I2 or Br2 are used as transport agents. Cl2 exists in the gaseous form in room temperature, which is rather dangerous. Instead, it can be supplied as metal halides compounds such as TaClx, MoClx, and PtClx. It is noticed that most of these materials are unstable or hygroscopic in an air environment, and hence an oxygen- or moisture-free environment is necessary. The CVT conditions for m-LTMdCs are listed in Table 3. The variables are growth temperatures (hot and cold zones), types of transport agents, transition metals, and chalcogens. Even if there is a transport agent, a temperature gradient is required for the deposition of materials as described in table.

The process enables the formation of single crystal at low temperatures. The solute is slowly solidified during cooling process and eventually crystallized and precipitated out into a single crystal. During the process, the reduction of the solute due to the solidification in the flux lowers the reaction temperature. Several m-LTMdCs have been synthesized with this approach.8,12,131,115,132 For examples, 1T′-MoTe2 and WTe2, which are representative m-LTMdCs, have been synthesized with Te and NaCl fluxes, respectively. In particular, MoTe2 has low (H- or α-, semiconducting) and high temperature (T- or β-, metallic) phases. Typically, a quenching (rapid cooling) process at a high temperature is required in order to obtain 1T′ phase MoTe2.8 3.1.2. Chemical Vapor Transport. Chemical vapor transport (CVT) is another representative approach for a single crystal growth in bulk form. A number of materials, from simple halide to complex multinary oxide-based compounds, have been synthesized by the CVT method including mLTMdCs. A typical experimental scheme is shown in Figure 5b. In this process, raw materials are transported to the substrate (if embedded) or inner wall of the ampule in the growth (cold) zone with the assistance of transport agents to form crystals. H (hot) and C (cold) indicate high and low temperature zones of the reaction tube in Table 3. The

3.2. Chemical Vapor Deposition

Chemical vapor deposition (CVD) provides LTMdCs as films. This conventional method has been widely adopted to implement high-quality LTMdCs on a large-scale film. The first CVD method we introduce here is the chalcogenization of thin (few to tens of nanometers) metal films on insulating substrates, which is referred to as the metal film CVD (MFCVD). In this method, a metal, which is one of the raw materials required to form LTMdCs, is preliminarily deposited as a film and then chalcogenized at a high temperature reactor. This approach has been conducted steadily since the early stage of CVD synthesis for LTMdCs. Figure 6a shows the schematic of typical MFCVD method. In detail, a few nanometers of Mo was deposited using a magnetron sputter or e-beam evaporator.119,120 Te vapor injection at high temperature convert the pure Mo to MoTe2 film. The process was firstly developed for the growth of MoS2 and adopted for the growth of other LTMdCs. The grown films are typically 6303


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LTMdCs such as 1T′-MoTe2, WTe2, and PtSe2 have been reported by the MFCVD method.105,119,135 On the one hand, it is advantageous to use oxide film instead of pure metal film. Phase controlled growth is an example. Oxide deposition (MoO3) enables 2H MoTe2 growth whereas 1T′ MoTe2 growth was preferred in pure metal chalcogenization.120 Because reactions favor a direction that minimizes volume change, 2H phase (47%) is preferable compared to 1T phase (380%) MoTe2 during MoO3 tellurization. On the other hand, with oxides, it is able to grow monolayer LTMdCs when a small amount of oxide is constantly codeposited with the chalcogen on the target substrate. This is beneficial to attain large grains of LTMdCs. Both techniques are named as metaloxide CVD (MOxCVD) (Figure 6b) in this review since we classify the types of CVD according to the chemical form of precursors. Growth of NbSe2 and 1T′-MoTe2 through this platform has been reported.120,139 This growth platform requires further validation for materials which has extreme evaporation temperatures such as HfOx (approximately 2500 °C). Oxides must be reducible during the growth process. Unlike the conventional CVD approaches, the metal-halide CVD (MHCVD) method uses metal halide precursors, which is also similar to CVT method. In particular, the use of metalhalides, in principle, coincides with the use of pure halogens such as Cl, Br, and I and metal elements in the CVT process. Then, the metal precursors transforms into the metal halides forms which can be easily vaporized. It eventually provides high-quality crystals. However, precursors are typically sensitive to oxygen and (especially) moisture in the air. Figure 6c shows the typical setup for MHCVD. S chips and HfCl4 powder are located in the inner tubes in the upstream zone. Because the HfCl4 precursor has a lower vaporization temperature (310 °C in the experiment), HfS2 (s-LTMdCs) was successfully grown with the method.140 Several mLTMdCs have been carried out by this approach. TiCl4, VCl4, ZrCl4, and NbCl5 used as metal-halide sources for the growth of TiS2 and TiSe2, VS2 and VSe2, ZrS2 and NbS2, and NbSe2, respectively. We also assign H2PtCl6 for the synthesis of PtSe2 in this category (see Tables 4 and 5) The metal−organic CVD (MOCVD) method was used in the 1990s for the synthesis of m-LTMdCs, notably for the production of TiS2 through the introduction of Ti(S-t-Bu)4.53 It is adventageous that the precursor has low decomposition temperatures compared to pure metals or oxides because the bonding between metal and organic component are weak. These materials are highly toxic and therefore should be handled with care. MOCVD has recently been adopted to synthesize s-LTMdCs (Figure 6d). Metal−organic precursors such as Mo(CO)6, W(CO)6, and (C2H5)2S were introduced for growing wafer-scale MoS2 and WS2.141 The approach has not yet been extended for the growth m-LTMdCs except 1T′MoTe2.142 Metal precursor can also be prepared as a solution type (water or organic liquid medium). For example, (NH 4 ) 6 Mo7 O 24 143 and (NH4 ) 2 MoS 4 144 are soluble in deionized (DI) water and organic solvent, respectively, followed by dipping or spinning on the substrate (liquid source CVD, LSCVD). Such materials eventually decompose into metal oxides form therefore annealing the substrate with (or without) extra chalcogens produces monolayer LTMdC or continuous film (few layers). A mixture of the metal oxide and its chloride can facilitate the metal−chalcogen reaction to create huge flakes−hybrid CVD (HCVD). In the work,127 metal oxide−metal chloride−Te precursor in a 1:1:1 ratio was

Table 3. Growth Conditions for the CVT Method with Various Transition Metals and Transport Agentsa CVT conditions metals

chalcogens

ref

H (°C)

C (°C)

TA

Ti

S

52, 44, 45

Se

52, 45, 55

Te

52, 45

900 800 900 900 780 880 900 750

800 720 700 800 740 790 800 690

I2 I2 I2, S I2 I2 Se2 I2 I2

Se

61− 65

850 870

800 780

Te

66

I2 Se2 I2

S

52, 67

Se

42,67

900 1010 900 900 850

850 930 850 800 800

I2 I2 I2 I2 I2

S

72

Se

76−78

800 850 700

Te

82−87

850 950 730 780 900 1000

I2 I2 I2 I2 I2 I2

Sn

S

52, 40

950 950

600 850

I2 I2

Hf

Te

88, 89

800 800

500

I2 I2

Ta

S

91−93

Se

97, 98

Te

100−102

850 950 700 725 1050 700 850

800 300 650 700 1000 650 750

I2 I2 Cl2 I2 I2 Cl2 Cl2

Pt

S

103

800

740

Cl2

Mo

Te

116−118, 11

1000 1000 1000

900 900 900

TeBr4 TeCl4 I2

W

Te

31, 133

750 950

650 775

Br2 Br2

V

Zr

Nb

850

a

H (hot) and C (cold) are the temperatures of the tube. TA is an abbreviation of transport agent.

thicker than the initially deposited metal film due to the volume expansion by metal-chalcogen reaction. In some cases, the approach induces cracking and surface roughening of the film. Control of the reaction speed can resolve this issue.119 Scalability and accessibility are the advantages of MFCVD method. However, the grain size is relatively small compared to other conventional approaches to be introduced. Few m6304


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Figure 6. Various chemical vapor deposition (CVD) methods for film and monolayer growth are shown. (a) Metal film (predeposited) CVD; MFCVD. Reproduced with permission from ref 119. Copyright 2015 American Chemical Society. (a) Metal oxide (predeposited) CVD; MOxCVD. Reproduced with permission from ref 120. Copyright 2015 American Chemical Society. (c) Metal halide CVD; MHCVD. Reproduced with permission from ref 140. Copyright 2016 IOP Publishing. (d) Metal organic CVD; MOCVD. Reproduced with permission from ref 141, Copyright 2015 Macmillan Publishers Ltd.. (e) Liquid source CVD; LSCVD. Reproduced with permission from ref 125. Copyright 2016 IOP Publishing. (f) Hybrid CVD (oxide and chlorine precursor); HCVD. Reproduced with permission from ref 127. Copyright 2017 Wiley.

formation of WTe2 on bilayer graphene graphitized from 6H-SiC(0001). It shows the semiconducting behavior at low temperatures.153 3.3.2. Li-Intercalation. Intercalation is the process that inserting the ions into a layered material. In LTMdCs, typically alkali metal ions have been used as guest materials, which induces structural changes due to the charge transfer from the guest (ion) to the host material (LTMdCs). For an example, phase transition from semiconducting 2H to metallic 1T phases takes place during the intercalation process in MoS2. Many applications using LTMdCs have been reported such as supercapacitors, batteries, and hydrogen evolution reaction (HER) catalysts.154,155 The phase transition by chemical treatment also applied to the bulk LTMdCs materials. One of the advantage is that Li intercalating compounds (or alkali metals) can chemically exfoliate bulk materials into several layers, even down to monolayers. The phase change occurs by modulating the electron injection from a semiconducting to a metallic one. For example, intercalation of Li-ion in MX2 (M, metal; X, chalcogen) can be described by the following reaction:

introduced at the downstream zone with extra Te vapor from the upstream zone to synthesize 1T′-MoTe2 and WTe2, which are both m-LTMdCs. Table 4 and 5 show various growth conditions for CVD approaches. 3.3. Other Synthetic Methods

3.3.1. Molecular Beam Epitaxy. Since the development of molecular beam epitaxy (MBE) in the 1960s, this technique has been widely adopted for ultrahigh quality film growth in the laboratories and industry. With MBE techniques, described in Figure 7a, growth typically carried out in ultrahigh vacuum (UHV) as high as 10−12 Torr with controllable growth rate which is precise, in principle. The purity (or quality) of film is extremely high compared to the achievements from the other synthetic approaches. The growth of vdW layered materials, including TMDs, by MBE was initially accomplished in the 1990s;146−150 several m-LTMdCs were successfully synthesized by MBE, as shown in the Table 5. The materials grown with MBE are therefore suitable for investigating intrinsic physical properties, which require high purity and crystallinity. For example, MBE grown TiSe2 sample clearly shows CDW phenomenon,57,59 which is discussed separately in other section of the manuscript. TaS2 layer was also successfully synthesized on Au (111) substrate.96 Layer controlled growth of PtSe2 by MBE method has been reported,106 and the material exhibits a high bulk conductivity and intriguing Dirac semimetallic properties.151,152 Monolayer NbSe2 grown on graphene and h-BN also shows CDW phenomena and superconductivity.106 In the case of MoTe2, a wide variety of substrates have been used as growth templates such as graphene,128 MoS2,106 and highly ordered pyrolytic graphite (HOPG).107 Bulk WTe2 is known to exhibit giant magnetoresistance. MBE process enables a monolayer

MX 2 + n BuLi → [MX 2− + Bu•+ Li+] → LiMX 2 + octane

The intercalating material in chemical reaction is n-butyl lithium, a partially converted metallic (1T) phase of MoS2 obtained from the semiconducting (2H) phase.108−112,114,156−158 Recent advances in phase transition (or engineering) offer degrees of freedom to obtain novel heterostructure for low contact resistance devices. For example, monolayer metal−semiconductor−metal device 6305


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Table 4. Growth Conditions for the CVD Process (Film)a experimental conditions for film metals

chalcogens

ref

type

source

temperature (°C)

shape

Ti

S

53, 54

Se

56, 57

MOCVD MHCVD MHCVD MBE

Ti(S-t-Bu)4 TiCl4 TiCl4 Ti metal

150, 270 200−500 250−600 200−300

rough film rough film plate-like film ultrathin film

S

60

MHCVD

550

SC nanosheet

Se

64

various types

VCl4 VOCl3 V(NMe2)4 VCl4

250−600

plate-like film

Zr

S Se

68 71

MHCVD ED

ZrCl4 ZrSO4

600−800 100−250 after deposition

thin film

Nb

S

73−75

Se

79

MHCVD MHCVD MHCVD MHCVD

NbCl5 NbCl5 NbCl5 NbCl5

1050 1000 800 250−650

SC thin flake SC thin flake SC nanosheet plate-like film

Hf

Te

90

MBE

Hf metal

530, 650

thin film

Ta

S

94, 95

Se

99

MHCVD CVT MBE

TaCl5 Ta metal Ta metal

820 950, 300 450, 650

SC thin flake film film

Pt

Se

104, 105

MHCVD MFCVD

H2PtCl6 Pt film

900 400

SC nanosheet thin film

Mo

Te

119−124

MFCVD MOxCVD MOxCVD MFCVD MOxCVD MOxCVD

Mo film MoO3 film MoO3 Mo film MoO3 MoO3 film

650 700 680 700 700, 650 650−800

thin film thin film film thin film film film

W

Te

134, 135

MFCVD MBE

W film W metal

800 275

film thin film

V

Abbreviations of “type” column are listed in Figure 6and the Abbreviations section.

a

structure of MoS2 was fabricated by n-butyl lithium treatment as shown in Figure 7b.114 Unusual electrical transport such as variable range hopping can also be induced by chemical treatment due to partial conversion of the phase of MoS2.112 3.3.3. Phase Transition by Laser and e-Beam Irradiation. There are other fascinating approaches for phase engineering of LTMdCs. Unlike Li intercalation, no chemical treatment is necessary for laser or e-beam induced phase transition in LTMdCs. Recent study showed a route to fabricate ohmic homojunction contact by laser-induced phase transition in MoTe2 with thinning process.10 The techniques have previously been reported for thinning the layered materials in graphene and MoS2.159−162 Figure 7c shows the schematic of laser-induced phase transition. Laser irradiation generates local heat in 2H-MoTe2. Because of the small energy difference between 2H and 1T′ phases in MoTe2, the irradiated site in 2H-MoTe2 changed to 1T′, forming an ohmic contact. The fabricated MoTe2 transistor with homojunction exhibits the improvement of the carrier mobility by a factor of 50 with an on/off ratio as high as 106. Phase transition from 2H to 1T was established in Re doped MoS2

under e-beam irradiation during in situ transmission electron microscope (TEM) observation.113 The 2H phase converts into a new intermediate phase as described α in the literature. In this case, the atomic arrangement of 2H phase gradually transformed to 1T phase, as shown in Figure 7d. These technique may offer pattern-able phase transition in future, which could be extended to industrial applications.

4. ELECTRONIC STRUCTURES 4.1. Electronic Structures of Representative Metallic Layered Transition Metal Dichalcogenides

Electrons form discrete energy levels in atoms. Electrons in molecules form a series of new electronic energy levels via the hybridization of orbitals, grouped as bonding (occupied) and antibonding (unoccupied) levels.163 Solids consist of a huge number of atoms, which generates a collection of discrete energy levels with small energy differences between them. These energy levels can be grouped into conduction and valence bands, similar to the unoccupied and occupied energy levels in molecules, respectively. If the atoms are arranged in an 6306


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Table 5. Growth Conditions for the Monolayer m-LTMdCs by Various CVD Processesa experimental conditions for monolayer metals

chalcogens

ref

type

source

temperature (°C)

shape

Ti

Se

58 57 59

MBE MBE MBE

Ti metal Ti metal Ti metal

220 200−300 450

Zr

S

69 70

MHCVD MHCVD

ZrCl4 ZrCl4

600−900 730−830

SC flake SC flake

Nb

Se

80 81

MBE MBE

Nb metal Nb metal

325 450−780

SC flake SC flake

Ta

S

96

MBE

Ta metal

Pt

Se

107 106

MBE

Pt metal

200−270

Mo

Te

125 126 127 128 129 130

LSCVD LSCVD HCVD MBE MBE MBE

AHMb AHM MoO3 and MoCl5 Mo metal Mo metal Mo metal

610 700 750−850 250−350 25−350 250−450

SC flake SC flake SC flake

W

Te

127 136 137,138

HCVD LSCVD MBE

WO3 and WCl6 AMTc W metal

750−850 650 250

SC flake SC flake

a

Molecular beam epitaxy (MBE) is also included. SC is an acronym of single crystal. bAHM: ammonium heptamolybdate. cAMT: ammonium metatungstate.

Figure 7. Other synthetic approaches. (a) Molecular beam epitaxy (MBE). Reproduced with permission from ref 81. Copyright 2016 AIP Publishing. (b) Li-intercalation. Reprinted by permission from ref 145. Copyright 2014 Macmillan Publishers Ltd. (c) Phase transition by laser irradiation. Reproduced with permission from ref 10. Copyright 2015 American Association for the Advancement of Science. (d) Phase transition by e-beam exposure. Reprinted by permission from ref 113. Copyright 2014 Macmillan Publishers Ltd.

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Figure 8. Classification of band structures of materials in k-space. (a) metal, (b) semiconductor, and (c,d) semimetals.

order, a crystal is formed. In such a case, the electronic structure can typically be described in the reciprocal or momentum, space (e.g., k-space).163 Figure 8 shows the general electronic band structures of materials in k-space with several different scenarios. If there is no overlap between the conduction and the valence bands (Figure 8a,b), which occurs when the number of electrons in the primitive cell is even, a band gap exists between these two bands, forming a semiconductor or insulator. The gap between the two bands is called the energy band gap. The Fermi level is located at the middle of the bandgap, in principle. If the number of electrons in the primitive cell is odd, the material becomes metallic because one energy band is partially occupied. Another situation is when there is a small overlap in the k-space between the conduction and valence band (Figure 8c), such that the concept of the conduction band and valence band is no longer clear anymore. In such a case, regardless of whether the number of electrons in the primitive cell is odd or even, the materials have metallic characteristics with a large number of free electrons at the Fermi surface. If the overlapped energy regime is small, these materials are called semimetal with a low electron and hole concentrations at the Fermi surface. These materials are interesting, having two different types of carriers: electron- and hole-like carriers, which give rise to a large magnetoresistance.164−166 The situation becomes more interesting when there is an intersection between the conduction and valence bands (Figure 8d). Topological insulators and Weyl semimetals fall into this category, which are discussed in the section 6.167−172 Because crystals are formed by a certain ordered arrangement of atoms, their electronic band structures are strongly correlated to their crystal structures (e.g., bond lengths, angles, and coordination) and the electronic configurations of the constituent elements.173 The crystal structure of the material is also determined by the electronic structures of the constituent elements. Although the prediction for the existence of compounds (e.g., chemical composition) and their structures is still challenging from the theoretical point of view, understanding the electronic energy of elements is a crucial step to build an intuitive picture of the properties of crystals. Figure 9 shows the relative energy levels of group IV, V, and VI transition metals compared to those of chalcogen atoms.173 Chalcogen atoms have six valence electrons in the s and p orbitals (s2p4), while transition metals have a wide range of electron configurations with the outermost electrons mainly located at d and s orbitals.

Figure 9. Relative energy levels of representative transition metals and chalcogen atoms. Reproduced with permission from ref 173. Copyright 1986 Springer.

The electron characteristics near the Fermi level of the LTMdCs are strongly determined by the interactions among electrons in the p, s, and d orbitals of each species. The energy level of the s orbital in chalcogen atoms is relatively deep in the valence band and does not significantly contribute to the band structure near the Femi level.173 The group IVB transition metals such as Ti, Zr, and Hf have four electrons in their outershell, two for each in the d and s orbitals with a d2s2 configuration. The most common phase of this group with chalcogens in LTMdCs is the 1T phase. Origin of such a 1T phase is little known at the moment. The change in the band structure of MX2 (M, metal; X, chalcogens) of group IV can be intuitively explained by considering the relative energy difference between metals and chalcogens. Because the total number of valence electrons in the unit cell is 10, an even number, this is likely to exhibit semiconducting property. In fact, HfS2, HfSe2, ZrS2, ZrSe2, and TiS2 are semiconductors.32,173 The energy level of the d orbital increases from Ti to Zr to Hf, which leads to a larger energy difference from the energy level of p orbital of chalcogens. Therefore, the bandgap between the conduction and valence bands increases, giving rise to a larger bandgap in HfS2 (HfSe2) compared to that of ZrS2 (ZrSe2).174,175 Similarly, the band gap decreases when S is replaced by Se. Eventually, semimetals are formed in Te compounds.173−176 TiSe2 is presumably similar to a semiconductor. However, the energy levels of the Ti d orbital and 6308


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Figure 10. (a) Calculated and (b) experimental ARPES of TiS2 and (c) the Fermi surface. Reproduced with permission from ref 187. Copyright 2015 Institute of Physics Publishing. (d) Calculated and (e,f) experimental ARPES of TiSe2. Reproduced with permission from ref 186. Copyright 2017 Elsevier.

Figure 11. (a) Hexagonal Brilluoin zone (b,c) low and (d,e) high resolution ARPES band structure of VSe2. (f−j) The Fermi surface slices of selected BZ planes. Reproduced with permission from ref 189. Copyright 2012 American Physical Society.

d5s1, which is the half-filled configuration. In contrast, the most stable form in W is d4s2. However, it is worth mentioning that the d5s1 configuration has a similar energy to d4s2 configuration in W.173 CrX2 is a metastable phase with a 1T structure, which does not appear in the equilibrium phase diagram of Cr-X.178 In contrast, WX2 and MoX2 share a common 2H stable phase with semiconductor characteristics at room temperature, excluding WTe2, which has a Td structure.31 The MoTe2 reveals a T′ (a distorted form of Td) phase at high temperature.8 The T′ phase can transform to the Td phase and vice versa by controlling the Te vacancy, temperature, or pressure.179 The metallic phases of WTe2 and MoTe2 are covered in the next section.

Se p orbital are very close to each other, leading to an overlap in the energy to form a semimetallic phase. We discuss the band structure of TiX2 later in this review. The LTMdCs formed by the group VB transition metals are always metallic due to the presence of odd number of electrons in their orbitals.173,177 VX2 is stable with a 1T phase, while both NbX2 and TaX2 have 2H phase. The 1T phases are stable at only high temperature.177 Instead, at room temperature, they transform to distorted phases. A lower symmetry structure belonging to the space group 12 of MTe2 is also observed in this group. The group VIB transition metals have six valence electrons. The most stable electron configuration of both Cr and Mo is 6309


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Figure 12. Band structure of 2H-NbSe2 and 1T-NbSe2. Reprinted with permission from ref 190. Copyright 2016 Macmillan Publishers Ltd.

4.1.1. 1T-TiS2 and 1T-TiSe2. The fundamental band structure of the bulk TiS2 and TiSe2 were undefined for a long time.173 This is because the experimental band structures cannot be easily obtained from the whole k-space; moreover, the simulation method for the band structure calculation usually underestimates the material bandgap.180−185 The band structures of bulk TiS2 and TiSe2 have recently been defined with the B3LYP hybrid functional, the MBJ potential, and a well-developed ARPES technique. Figure 10 shows the calculated and experimental band structures of 1T-TiS2 and 1T-TiSe2.186,187 In TiS2, there is no overlap between the conduction and valence band. Therefore, TiS2 is a semiconductor with a small indirect band gap of 0.53 eV, where the maximum (minimum) of the valence (conduction) band is located at the Γ point (M point). The simulation and experimental data are quite consistent, although a smaller gap (0.4 eV) is predicted from the simulation result, as shown in Figures 10a,b.187 A small electron pocket in the conduction band emerges at the M point due to the n-doping effect of the S vacancies, which are formed during the crystal growth, leading to six Fermi contours at the M points, as shown in Figure 10c. In contrast to TiS2, a small overlap between the valence and conduction bands between Γ, A. and L points appears in TiSe2 (Figures 10d−f). As a consequence, TiSe2 is a semimetal with an electron pocket near the L point and a hole pocket at the Γ point.186 4.1.2. 1T-VSe2. Vanadium belongs to group VB in the periodic table. There is one more electron in the unit cell of 1T-VSe2 compared to 1T-TiSe2. Therefore, it is obvious that 1T-VSe2 is metallic with a partially filled band.173,188,189 Figure 11 shows the band structure and Fermi surface of VSe2 measured by ARPES with the soft X-ray at 10 K.189 It is clear that the Fermi level crosses the band along the Γ−K direction (Figure 11e), indicating the metallic nature of VSe2. Along the z direction (Γ−A), the band dispersion is smaller than that in the in-plane directions (Γ−M and Γ−K). There are two relative flat bands with small dispersion, one is near the Fermi level and another is approximately 2 eV below the Fermi level. The Fermi surface of VSe2 is a closed surface with six loops. Parts f and g of Figure 11 show the calculated and experimental Fermi surface in different planes. The theoretical simulation agrees well with the experimental data. 4.1.3. 1T- and 2H-NbSe2. Although Nb belongs to group VB similar to V, NbSe2 has two crystal structures, 1T and 2H phases.173,177 Both of these are metallic because of the odd number of valence electrons in Nb. However, the 1T phase is not the most stable phase of NbSe2 at room temperature.177

There is a phase transition from 1T phase to its distorted phase that is stable at room temperature.177 Therefore, to determine the band structure of the 1T phase, measurements should be performed at high temperatures. The band structure we discuss here is not that of the 1T phase but of its distorted phases. Figure 12 shows the band structure of a mixture of the 2H and 1T phases at 40 K, where the distorted phase of the 1T structure has been formed.190 The mixed sample of 1T and 2H phases is synthesized by annealing the coevaporation film of Nb and Se atoms on bilayer graphene/6H-SiC (0001) at 530 °C. Compared to the bulk 2H phase (Figure 12b), several additional bands appear, denoted as the band structure of 1T phase with a red curve (Figure 12a). Interestingly, the flat band (α band) does not match with the DFT simulation for 1T phase, indicating the Mott−Hubbard band in the Mott insulator phase.190 This implies that the distorted phase reveals the Mott insulator in the 1T phase structure. We discuss this in detail in the PLD section. 4.1.4. 1T-, 2H-, and 4H-TaS2. In addition to the structural differentiations between compounds with the same chemical composition, an interesting feature of LTMdCs is the formation of different stacking sequences along the cdirection.173 TaS2 displays both 1T and 2H structures. The 4H polytype is a combination of the 1T and 2H phases, which has four layers, two layers each of the 1T and 2H structure.173,33−41 Therefore, the band structure and properties of 4H phase are a mixture of those of the 1T and 2H phases.33,35−41,173,191 The band structures of 2H-, 1T-, and 4HTaS2 are shown in Figure 13. The Fermi level cuts through the two (one) bands in 2H (1T) phase with two (one) layers in the unit cell. In the 4H structure, there are four bands, two from 1T and two from 2H. The two types of bands intersect along the M−K direction. The interaction between these bands lead to new properties of the 4H phase, which do not appear in the 1T and 2H phases. However, the 4H phase as yet remains elusive. 4.2. Layer Dependence of the Band Structure in Metallic Layered Transition Metal Dichalcogenides

Although the interaction between the layers in LTMdCs is the weak van der Waals force, this interaction still plays an important role to construct the band structures and properties of LTMdCs as well as 2D materials.192−196 An obvious piece of evidence is that the band dispersion along Γ to A of many bands is still not negligible.23,197,198 As a consequence, the band structures of LTMdCs are strongly dependent on the number of layers. Figure 14 shows the band structure of TiSe2 from monolayer to six-layer samples of the normal and CDW 6310


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5. PERIODIC LATTICE DISTORTION OR CHARGE DENSITY WAVE IN MATALLIC LAYERED TRANSITION METAL DICHALCOGENIDES 5.1. Periodic Lattice Distortion Phenomenon

In many metals, the phase with the primitive cell structure (called the normal phase) is unstable when the temperature is lowered.177,202−206 Their structures distort to form new structural phases, known as the periodic lattice distortion (PLD) phase (or the charge density wave (CDW) phase).206 The name CDW does not clearly reveal the physical intuition of the distorted phase because the waveform of the charge density originating from the periodic arrangement of atoms does exist even in the normal phase.202,203 Therefore, we prefer to use the name PLD rather than CDW in this review. The phenomenon of PLD occurs in many 2D layered metallic materials.177 The temperatures of the PLD transitions have a wide range, differing between materials.177 Additionally, one material can have many different transitions. The structure of the PLD phase can be commensurate (C) or incommensurate (IC) with the normal structure. Figure 16a shows the distorted structure of TaS2 at a low temperature. The size of the unit cell in the C-PLD phase is 13 × 13 of the normal phase, as shown in Figure 16a.177 In TaS2, there are three transitions: from the normal phase to the IC phase at 543 K, from the IC to the nearly commensurate (NC) phase at 353 K, and from the NC to the C phase at 190 K.177 The schematic corresponding to each phase transition is summarized in Figure 16b.92 The position of the atoms in the PLD phase is slightly distorted from the original position, which can be revealed from TEM and scanning tunneling microscope (STM) observations (Figure 16c−e).207,208 It is worth noticing that the amplitude of the distortion is very small (∼0.1 Å) compared to that of the normal structural phase transition, which generates a completely different crystal structure. The PLD transition is always accompanied by a softening phonon, called the lattice instability, which is discussed further in the next section.177 Figure 17 shows another example of the PLD transition in TiSe2.210−212 There is only a transition at 200 K from the normal phase to the distorted one with 2 × 2 × 2 structure. Interestingly, TiSe2 has domains with different chiralities (clockwise and anticlockwise) in the PLD.211 The formation of these different domain structures can be understood by relying on the distorted structure of Se on the top and bottom layers in the 2 × 2 × 2 lattice. Along with the in-plane distorted structure, there is relative movement of Se atoms on the top and bottom layers, marked with red and blue arrows, respectively.210 It can be seen that the directions of top and bottom layers are opposite, one is clockwise and another is anticlockwise. The roles of the top and bottom layers is interchangeable, giving rise to domains with different chiralities in real space (as shown in Figure 17d).211

Figure 13. Band structure of (a) 2H-, (b) 1T-, and (c) 4H-phase of TaS2. Reproduced with permission from ref 173. Copyright 1986 Springer.

phases.194 With the few layers, the Γ (M) and A (L) points are same. The overlapping between the top valence and bottom conduction bands at Γ and M points increases as the number of layers increases for both the normal and CDW phases. Consequently, a large band overlap is clearly shown between the A and L points in bulk. The interlayer interaction becomes more dominant in group VIIIB (Ni, Pd, Pt). The metallic nature of the bulk can transform to semiconducting characteristics in the few layer sample.199 Figure 15 shows the band structures of mono and bilayer PdS2. While bilayer PdS2 is a semimetal, the monolayer is a semiconductor with a bandgap of 1.1 eV. This phenomenon is caused by the strong vdW interlayer interaction, which makes the conduction band more dispersed, overlapped with the valence band, implying the semimetallic or metallic behavior. The phenomenon occurs in other type of layered materials such as GeP3 and antimonene (Sb) and is expected to reveal in other layer materials with a strong vdW interaction.200,201 This interesting phenomenon could lead to the design of a metal−semiconductor contact without any physical boundaries.199 In addition to the variation of band gaps or the types of band structures (metal or semiconductor), many other properties can be changed when decreasing the thickness of materials such as the PLD, magnetism, and superconductivity. We will discuss these issues in the next chapters.

5.2. Mechanism for Periodic Lattice Distortion Transition

The instability of a one-dimensional metal at low temperature was first proposed by Rudolf Peierls.202,203 Because of its intuitive and simple nature, the Peierls model is typically used to explain the PLD transition in many text books and is a good starting point before going to the introduction of a complicated microscopic theory. We explain here why this simple model is not applicable in many cases when studying real 2D materials. Figure 18a shows the band structure of one 6311


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Figure 14. Layer-dependent band structure of TiSe2 from monolayer to six layers. (a) Normal phase, (b) periodic lattice distortion (PLD) wave phase, and (c) simulated band structure of normal and PLD phases. Reproduced with permission from ref 194. Copyright 2016 American Chemical Society.

unoccupied states (more precisely, the electrons are redistributed to states both below and above the Fermi level, following the Fermi−Dirac distribution), which has higher energies than the unoccupied states in the normal phase.206 As a consequence, the energy difference in the distorted phase compared to the normal phase is reduced when the temperature is increased, leading to a transition to the normal phase at high temperatures. Why does the distortion take place at 2a and not at 3a or 4a? Assuming the distortion happens at 3a, the gap will form at the π ± 3a position, located below the Fermi level. Both the lower and higher energy states are occupied, and hence, no energy gain is obtained in this case. This is the reason why it is believed that the PLD transition is always accompanied by a metal−insulator transition, with the gap opening at the Fermi level.202,203 However, this situation is only applicable for a oneband model. In real materials, the electronic band of the normal phase is degenerate. A small distortion will differentiate the degeneracy of this band, and the energy change can be not the same as that of one band. In many cases, the total energy distribution of electrons to this band will lower the energy as shown in the right panel of Figure 18c without any formation of a band gap at the Fermi level. Figure 19 shows two different cases for the PLD phases of TiSe2 and 1T-TaS2, where the energy gap is generated below and at the Fermi level, respectively.58,209 In TiSe2, the PLD phase have 2 × 2 × 2 supercell, and their Brillouin zone (red) is smaller than that of the normal phase (blue) (Figure 19a). The M point of the normal phase is folded to the Γ point of the PLD phase. As a consequence, the electron band of the normal phase at the M point appears at the Γ point in the PLD phase, which is clearly shown in Figure 19b. The electronic band at the Γ and M points are lower in the PLD phase compared to the normal phase, indicating a reduction of the

Figure 15. Band structure and density of states of mono- and bilayer PdS2. Reproduced with permission from ref 199. Copyright 2016 John Wiley & Sons.

electron model of a 1D periodic potential with a lattice constant a in the first Brillouin zone.202,203,206 In this model, the electronic band is half-filled, which indicates that the Fermi π level intersecting the band at ± 2a . However, this metallic band is not the minimum energy structure. If the structure is slightly distorted, forming a periodic potential with 2a, the band π structure will have a gap at the position ± 2a at the Fermi level, as shown in Figure 18b. Because the occupied states, which locate below the Fermi level, have lower energy compared to those of the undistorted phase, the distorted structure is more stable than the normal structure. At higher temperatures, the electrons below the Fermi level will be thermally excited to the 6312


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Figure 16. Periodic lattice distortion in 1T-TaS2. (a) The schematic of the relative movement of the commensurate PLD phase compared to the normal phase. Reprinted with permission from ref 209. Copyright 2015 Macmillan Publishers Ltd. (b) Schematic of formation of different transition phase in 1T-TaS2. Reproduced with permission from ref 92. Copyright 2015 American Association for the Advancement of Science. (c,d) The TEM image of the C-PLD phase, which clearly reveals the star shape of the C-PLD phase. Reprinted by permission from ref 208. Copyright 2010 Macmillan Publishers Ltd. (e) STM image of the C-PLD phase. Reproduced with permission from ref 207. Copyright 2016 Cornell University Library.

gives rise to the concept of Fermi surface nesting, where the electron screening suddenly changes in q space. The physical quantity directly related to Fermi surface nesting is the bare electronic susceptibility, expressed by213

electronic energy. A similar trend is also observed at the L point.186,210 In fact, no gap is formed at the Fermi level. Many similar examples can be found in other materials such as 2HNbSe2 and 2H-TaS2.210,213 It is noticed that the proposed excitonic mechanism in TiSe2 is not suitable for this case because all changes in the band structure occurs below the Fermi level.214,215 The time-resolved X-ray spectroscopy also excludes the excitonic mechanism.216 Figure 19c shows the experimental (left) and calculated (right) band structures of the C-PLD phase of 1T-TaS2. In contrast with the TiSe2 case, a gap is generated in the C-PLD phase of 1T-TaS2 along all in-plane directions, although there is still an electronic band intersecting the Fermi level along the Γ−A direction,.209 In addition, the 1T-TaS2 is a strong electron-correlated system and the Mott transition is proposed to explain the PLD formation.208,217 However, a softening of the phonon modes does reveal in the DFT simulation without consideration of the strong correlation effects, indicating the significant effect of the variation of electronic energy following the lattice distortion, named electron−phonon coupling.218−220 The general driving mechanism to minimize the electronic energy in both cases is similar to the Jahn−Teller effect in chemistry.221 It is worth mentioning the concept of the Kohn anomaly together with Fermi surface nesting and how these correlate to the Peierls distortion. The Kohn anomaly is a phenomenon, wherein the phonon spectrum is softened due to the reduction of electron screening at a certain k-point.222 In the 1D model, the softening of phonon occurs at q = 2kF. The softening of the phonon due to the Kohn anomaly is consistent with the instability of the one-electron model in Peierls distortion that generates the 2a supercell of the PLD phase.31,202,203,210 This

X 0(q) ∼ 2 ∑ ∑ nn′

k

0 f 0 (En0′ k − q) − f 0 (Enk ) 0 Enk − En0′ k − q

This quantity is only dependent on the Fermi surface and temperature. As mentioned above, the PLD can occur without a gap opening at the Fermi level in real materials. In such cases, the concept of Fermi surface nesting has a completely unphysical meaning and hence cannot be used to represent the PLD transition. Even with the case of the gap opening, there are too many distinguishing features between the Kohn anomaly and PLD transition.213 One representative difference is that the energy gain due to the Peierls distortion is contributed from the energy spanning across a wide range of kspace, while the Kohn anomaly sharply occurs at a specific kpoint. Therefore, we do believe that the concept of Fermi surface nesting should be used carefully for explaining the PLD transition, as clarified below. To study the phase transition, a macroscopic theory based on the free energy should be considered. The theory of electronic free energy for the explanation of the PLD phase transition has been developed for several decades.177 In this approach, the energy of the distorted phase can be expressed by F = F0 + ΔF

where F0 is the energy of the normal phase and ΔF is the energy change due to the distortion. This ΔF is dependent on the q vector and phonon mode λ, expressed by 6313


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Figure 17. Formation of the PLD domain in TiSe2. (a−c) STM and corresponding fast-Fourier transform images of the distortion phase of TiSe2. (d,e) Explanation of the chiral domain formation in TiSe2. The relative movement of Ti (cyan) and Se (yellow) compared to the normal phase. The red (blue) arrows indicate the distortion of the top (bottom) layer. The movement of the top and bottom layers is interchangeable, which can happen in the same layer but in a different area in real space, giving rise to the formation of chiral domains. Reproduced with permission from refs 211 and 210. Copyright 2010 and 2015 American Physical Society, respectively.

Figure 18. (a−c) 1D Peierls distortion.202 (d) Extended model for multiband model that typically happens in real materials.

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Figure 19. (a,b) Band structure of the distortion phase of TiSe2. The band of the Γ point of the normal phase is folded into the M point in the distortion phase. No band gap is generated at the Fermi level. The energy level at the Γ and M points decreases. Reprinted with permission from ref 58. Copyright 2015 Macmillan Publishers Ltd. (c) Experimental ARPES (left) and DFT simulation (right) band structures of 1T-TaS2. Reprinted with permission from ref 209. Copyright 2015 Macmillan Publishers Ltd.

1 1 ΔFqλ = − χ (qλ)|Q qλ|2 + D2(qλ)|Q qλ|2 2 2

The PLD transition is always accompanied by the softening of at least one phonon mode at a certain q point.177 This characteristic can be measured by inelastic scattering, which can directly observe the phonon spectrum of materials.223,224 Figure 20a shows the experimental phonon dispersion of 2HNbSe2, which clearly reveals the softening of the acoustic phonon mode when the temperature is lowered to the transition temperature, 33 K.223 The energy of the phonon is completely zero at this temperature, indicating the PLD transition. At a lower temperature, the phonon mode appears again, which is the phonon mode of the new PLD phase. The PLD transition of TiSe2 can be detected by X-ray thermal diffuse scattering.224 The intensity of the measurement at the L-point suddenly increased when the temperature reaches to 190 K, indicating the transition from the PLD phase to the normal phase. This phonon softening can also be revealed in the theoretical DFT simulation.225 It is notable that the electronic temperature describing the thermal excitation of the electrons can be included in the total free energy calculation. This factor is known as the smearing factor, which is normally used for a convergence of the numerical issue in DFT. The phonon spectrum of the normal phase dramatically changes with the smearing value. This is clearly shown in 2H-NbSe2, TiSe2, and other PLD materials.223,225

The first factor is related to the electronic change and the second term related the elastic distorted energy due to the distortion. Parameter χ(qλ) is called the generalized electronic susceptibility: X 0(q) = 2 ∑ ∑ nn′

k


|V1λ(nk , n′k − q)|2

where Vλ1 is a factor relating to the k and q vector electron− phonon coupling strength. If Vλ1 is not dependent on the k and q vectors, the generalized electronic susceptibility is proportional to the bare electronic susceptibility: X 0(q) ∼ 2 ∑ ∑ nn′

k


It is clear that the concept of bare electronic susceptibility concept can only be applied to study the PLD transition where Vλ1 is k- and q-independent, which is not easily satisfied in real materials. This condition may take place easier in 1D materials, where the nesting concept has been changed to imperfect nesting concept.205 6315


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Figure 20. (a) Evolution of phonon dispersion with temperature in 2H-NbSe2. A softening of the acoustic phonon mode is clearly revealed. Reproduced with permission from ref 223. Copyright 2011 American Physical Society. (b) The evolution of the X-ray thermal diffuse scattering intensity of TiSe2 with temperature along the A−L−A line with coarse and fine scans (inset), which shows a strong Bragg peak below 190 K. Reproduced with permission from ref 224. Copyright 2001 American Physical Society. (c,d) The simulated phonon dispersion of (c) 2H-NbSe2. Reproduced with permission from ref 223. Copyright 2011 American Physical Society. (d) TiSe2. Reproduced with permission from ref 210. Copyright 2015 American Physical Society.

Figure 21. Evolution of resistance with temperature in (a) TiSe2. Reproduced with permission from ref 232. Copyright 2017 American Chemical Society. (b) 1T-TaS2. Reprinted by permission from ref 234. Copyright 2014 Macmillan Publishers Ltd.

5.3. Experimental Characterization of Periodic Lattice Distortion

the resistance, the transition in TaS2 is very sharp with a huge hysteresis. In TiSe2, it is necessary to take the derivative of the R−T curve to determine the transition temperature, which is approximately 200 K. The transition of TaS2 is clearly shown in the R−T curve at 353 and 230 K, consistent with the XRD and STM studies. The different behaviors between TiSe2 and TaS2 may be explained by the different characteristics at the Fermi level in band structure of the PLD phase as mentioned earlier. The hysteresis is typically represented for a metal− insulator transition.

In addition to the direct structure characterizations such as STM or XRD and TEM, the PLD transition can also be detected by indirect methods such as electronic transport and Raman scattering.226−234 Although there is no common feature among different materials, the characteristic of the resistance with temperature (R−T curve) shows an abnormal metallic behavior.227,232,234 Figure 21 shows the R−T curves of TiSe2 and TaS2.232,234 While the TiSe2 shows a smoothly change of 6316


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Figure 22. (a,b) Evolution of Raman spectroscopy in 2H-NbSe2. (c−e) Evolution of Raman spectroscopy in 1T-TaS2. Reprinted by permission from ref 233. Copyright 2015 Macmillan Publishers Ltd. Reproduced with permission from ref 227. Copyright 2016 American Physical Society.

When the transition to the PLD phase occurs, the distortion reduces the symmetry of the materials, giving rise to new active Raman modes. By monitoring the appearance of these peaks, the phase transition can be determined.227,228,232,233 Figure 22 shows the evolution of Raman spectra of 2H-NbSe2 and 1TTaS2 with temperature changes.227,233 The appearance of new peaks near 30 and 200 cm−1 in 2H-NbSe2 are clearly observed during cooling down. The corresponding intensities of the softened peak are collected in the Figure 22b with different sample thicknesses. The transition temperature can be extrapolated from on the change in the peak intensity. The Tc is clearly incremented when the thickness of the sample is reduced. This method is rather difficult in experiments because a strong intensity of the Raman peak is required to reduce the error during extrapolation. Another approach based on the peak position is more accurate determination of Tc, as proved in the cases of TiSe2 and TaS2.227,232 In this approach, some Raman peaks even in the normal phase show a nonmonotonic variation. The Tc of TaS2 for the C-PLD transition was determined to be 140 and 21 K by decreasing and increasing the temperature, respectively. This is consistent with the transport measurement.

transition. For almost 2D metallic systems, it is widely accepted that the Bardeen−Cooper−Schrieffer (BCS) superconducting theory covers the physics behind this.235,236 Both BCS superconductivity and PLD transitions are related to phonons, and their interactions with electrons.237−241 Therefore, the study of the phonon spectra of the 2D metallic systems contains rich physics related to superconductivity and PLD via phonon−electron coupling. There are two approaches for tuning PLD transition and BCS superconducting phase: to control the carrier density by doping or to use pressure.230,242 Figure 23a shows the magnetic susceptibility of Cu-doped TiSe2, which exhibits a drop near the PLD transition. The transition occurs at a lower temperature with increasing the Cu content. The resistivity also reveals the same trend up to 0.6% Cu. At 0.6% Cu, the superconductivity appears with a resistance drop at 2 K. The critical temperature, Tc, increases further with increasing dopant concentration and reaches the maximum transition temperature at 4 K with 8% Cu. These behaviors of PLD and superconductivity also emerges by applying pressure, as shown in Figure 23c.230 Figure 23d summarizes the dome shape of TiSe2 by tuning the dopant and pressure. The doping has a stronger effect compared to that of pressure in this case. It is interesting to see how the phonon changes when the PLD is suppressed. Figure 24 shows the evolution of the Raman spectrum, measured at 3.5 K, with pressure.228 The Eg (70 cm−1) and A1g (110−140 cm−1) modes of the PLD phase are suppressed with increasing pressure, indicating a melting of the PLD transition. Although the simulation data of the phonon spectrum of TiSe2 by density functional perturbation theory

5.4. Tuning Periodic Lattice Distortion Transition and Superconductivity Phase Formation

In addition to the interesting physics behind the PLD transition, this transition occurs in many systems and can be tuned to display superconductivity. The common “superconductivity dome” shape, which happens in all types of superconductors, does reveal in materials showing the PLD 6317


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Figure 23. (a,b) Magnetic susceptibility and resistivity of Cu-doped TiSe2 at different temperature. Reprinted with permission from ref 242. Copyright 2006 Macmillan Publishers Ltd. (c) Resistivity of TiSe2 under different pressures and temperatures. (d) Superconductor dome shape of TiSe2. Reproduced with permission from ref 230. Copyright 2009 American Physical Society.

Figure 24. (a) Evolution of the Raman spectrum of TiSe2 at 4 K under different pressures. Reproduced with permission from ref 228. Copyright 2003 American Physical Society. (b) Calculated phonon dispersion of TiSe2 at 5 GPa. The softened phonon mode is still reserved but maintains real at low electronic temperature, indicating the suppression of the distortion phase. Reproduced with permission from ref 210. Copyright 2015 American Physical Society.

phase but not as strong as in TiSe2.243 As shown in Figure 25, the PLD transition is strongly tuned while the superconductivity transition is unaffected. This can be explained by considering the coupling of these two-phase transitions with the phonon. While the PLD is strongly coupled with the longitudinal acoustic mode, the superconductivity state is

also shows the softening mode at the L and M points, the real value is maintained, implying the stability of the normal state at low temperatures.225 Similar effects of pressure are also observed in 2H-TaS2 and 2H-TaSe2, however, the situation is different in 2H-NbSe2. Some degree of correlation is observed between the PLD state and the superconducting 6318


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state has a tendency to be suppressed in the thin samples with a reduction of the transition temperature.234,244 The carrier concentrations of the metallic state can be controlled by external doping methods with few layer samples such as the common oxide gate structure and surface doping by molecules. Figure 27a shows the phase diagram of 1T-TaS2 with different gate bias, which controls the carrier density of the sample.234 At low temperatures, a clear transition from the C-PLD to the NC-PLD and to the SC phase can be seen with increasing the gate bias. The superconducting phase disappears when a higher bias is applied, again forming a superconducting dome shape. The similar trend is observed in TiSe2 (Figure 27b).246 This approach is much advantageous for investigating the carrierdependent properties compared to the normal bulk approach, in which the strong interaction forming the new bonding state is difficult to exclude. Figure 25. Superconducting dome in NbSe2. A weak correlation between the PLD and superconducting phase is shown. Reproduced with permission from ref 243. Copyright 2015 American Physical Society.

6. OTHER PROPERTIES

strongly coupled with both the longitudinal acoustic mode and the optical phonon modes.243 This is the difference compared to TiSe2, in which the both quantum phases are coupled with the same acoustic phonon.236 An important property of 2D m-LTMDs is that the number of layers can be controlled by a simple scotch tape method.232−234,244,245 The thickness-dependent properties are also interesting for the study of the quantum phase at the 2D limit. This approach have been researched for a long time, showing that the superconducting transition temperature is reduced when the thickness of 2H-NbSe2 decreases.245 However, the PLD phase is stabilized at higher temperature when the thickness of the sample is decreased, as shown in Figure 26a. This trend is inverted in 1T-TaS2, where the PLD

6.1.1. Magnetism in 2D Materials and Magnetic Metallic Layered Transition Metal Dichalcogenides. The absence of 2D magnetic material has been predicted from the 2D isotropic Heisenberg model by Mermin−Wagner theorem. However,247 magnetically ordered states such as ferromagnetism (FM) and antiferromagnetism (AFM) have recently been discovered in monolayer 2D materials such as semiconducting FM CrI3, semiconducting AFM MPS3 family (M is Ni, Fe, Mn), and metallic FM GdAu2.192,248,249 2D magnetic materials have a number of advantages. Most van der Waals magnets have an intrinsic magnetocrystalline anisotropy owing to the reduced crystal symmetry, which is a promising candidate for future spintronic materials.

6.1. Magnetism in 2D Metallic Layered Transition Metal Dichalcogenides

Figure 26. Effect of thickness on the PLD and superconducting phase transitions in (a) 2H-NbSe2 and (b,c) 1T-TaS2. Reprinted by permission from refs 233 and 244. Copyright 2015 Macmillan Publishers Ltd. 6319


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Figure 27. Gate-controlled phase transitions in (a) 1T-TaS2 and (b) TiSe2. Reprinted with permission from refs 244 and 246. Copyright 2015 Macmillan Publishers Ltd.

Table 6. List of Magnetic LTMdCs (MX2) Materials with Basic Magnetic Propertiesa materials

space group

experimental or theory

structure

magnetic ordering

Tc or Nc (magnetic moment)

VS2 VSe2 VTe2 CrS2 CrSe2 CrTe2 CoS2 CoSe2 FeS2 FeTe2

P3̅m1 P3̅m1 P3̅m1 P3̅m1 P3̅m1 P3̅m1 Pa3̅ Pa3̅ P3̅m1 Pnn2

experimental theory experimental theory theory theory experimental experimental theory experimental

thin flake monolayer bulk bulk bulk bulk bulk bulk monolayer thin flake

FM FM AFM FM AFM FM FM FM FM FM

RT (0.51 μB/V atom) 514 K (0.68 μB/V atom) 410 K (−) ∼550 K (−) 120 K (0.84 μB/Co atom) 50 K (8.4 μB/g) 144 K (−) RT (−)

a

Tc (TN) indicates Curie (Néel) temperature.

ization versus magnetic field curves for thin VS2 and bulk VS2· NH3 are shown in Figure 28b. Both the thin and bulk VS2 show paramagnetic behavior in the high magnetic field region, while only thin VS2 shows hysteresis in the low field region, which is one of the main clues for ferromagnetism (zoomed graph in the inset of Figure 28b). Figure 28c shows a clear saturation of magnetization after subtracting signal from paramagnetic background. The trend of decreasing in the saturated magnetization (Ms) and coercivity (Hc) with increasing temperature further confirms the FM state in thin VS2. Temperature dependence of magnetization for thin VS2 nanosheets are shown in Figures 28d,e. The difference between zero-field cooling and field cooling at 100 Oe up to 330 K indicates the existence of a magnetic state below 330 K, as shown in Figure 28d. Under the high magnetic field (8000 Oe) (Figure. 28e), magnetic moment rapidly enhanced in the low temperature region (below 50 K) compared to the high temperature above 50 K because the paramagnetic and FM signals are mixed. A fitted curve summing the T3/2 law Curie− Weiss law for the FM and the paramagnetic state is shown in Figure 28e, respectively, as described by the following equation:

A list of m-TMdCs in Table 6 provides information on magnetic properties such as type of magnetic ordering, Curie (Néel) temperature, and magnetic moment. It should be noted that some of TMdCs are not layered structures, although they are in a form of MX2 such as CoS2 and FeS2. Among the TMdC materials listed in Table 1, only monolayer vanadium dichalcogenides (VX2 where X = S, Se, and Te) are magnetic layered materials. Although chromium dichalcogenides (CrX2) are also layered structures, they are metastable and mainly exist as a stable form of Cr2X3 in nature. In this regard, we will mainly discuss on MX2 with the layered structures. 6.1.2. Ferromagnetism in Atomically Thin 2D Metallic Layered Transition Metal Dichalcogenides (VS2 and VSe2). Vanadium dichalcogenides (VX2) have been predicted as long-range FM ordered materials by first-principles calculations even at monolayer thickness.43,250−253 The density of states and the atomic site projected density of states of VX2 (VS2 and VSe2) are presented in Figure 28a. The difference between the up and down spin states of VX2 indicates that monolayer VX2 is a ferromagnetic material. The d states of V atoms are highly delocalized and hybridized with the p states of S and Se atoms, indicating covalent bonding between the V and X atoms. Ferromagnetism is mainly contributed by V atoms, whereas X atoms contribute waekly to the total magnetic moment. Parts b−d of Figure 28 display experimental data from ultrathin VS2 flakes.43 The magnet-

M(T ) = Ms0(1 − AT 3/2) + CH /(T − θp) 6320


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Figure 28. (a) Density of states for monolayer VS2 and VSe2. The magnetism mainly originates from the V atoms. Reproduced with permission from ref 250. Copyright 2012 American Chemical Society. (b) Magnetization of thin and bulk VS2 (VS2·NH3) at room temperature, which shows a hysteresis in the inset. (c) Paramagnetic signal-subtracted curves for thin VS2 at various temperatures. The inset shows the temperature dependence of Ms and Hc. (d) Field cooling and zero field cooling curves for thin VS2. (e) Temperature dependence of magnetization of the thin VS2 fitted by summing the FM and paramagnetic behavior. The inset shows zoomed curves from 250 to 350 K. (f) Magnetoresistance of thin VS2 as a function of the magnetic field at room temperature. Reproduced with permission from ref 43. Copyright 2013 Royal Society of Chemistry.

where C is the Curie constant, θp is the paramagnetic Curie temperature, Ms0 is the saturated magnetization at 0 K, and A is a structure-related coefficient.254,255 The extracted value of θp is negative sign (−6.6 K), indicating the coexistence of the AFM with FM phases.43 Thin VS2 also has a negative magnetoresistance of 6.5% at room temperature with a magnetic field parallel to the electrical current direction. The clear hysteresis in the magnetoresitance implies the FM behavior of VS2 nanosheets (Figure 28f). Although some experimental data show the magnetic properties of VSe2, their origin is rather ambiguous. The magnetic behavior might be induced by defect creation during the synthesis process or substrate effect. However, the monolayer VSe2 growth by the MBE was recently demonstrated on the 2D substrate (e.g., graphite and MoS2), which

shows the magnetic hysteresis.256 This observation removes all ambiguities of the chemical synthesis approach. It consolidates again the power of the theoretical prediction in 2D materials. Similar to VSe2, the 1T-TaS2 is predicted as a magnetic semiconductor in the PLD phase, which reveals that the conduction and valence bands have different spin states.257 Figure 29 shows the band structure of bulk and monolayer TaS2 in the normal and PLD phases. In the normal phase, the band structure of monolayer TaS2 is similar to the in-plane band structure of the bulk TaS2. No significant change is observed, as shown in Figure 29a,b. However, the spinpolarized band appears in the monolayer of the PLD phase, whereas the bulk prefers the no-spin state in Figure 29c,d. This prediction has not yet been proven by experimental study, to date. 6321


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Figure 29. Band structure of (a) bulk and (b) monolayer TaS2 in the normal phase and (c,d) PLD phase. Reproduced with permission from ref 257. Copyright 2014 American Physical Society.

Figure 30. (a) Calculated magnetic moment per V atom and X (S and Se) atom as a function of applied strain for monolayer VX2. (b) Energy difference between the FM and AFM state of monolayer VX2 as a function of applied strain. Reproduced with permission from ref 250. Copyright 2012 American Chemical Society. (c,d) Magnetic moments of S (Se) (c) and Nb atoms (d) for monolayer NbS(Se)2 as a function of applied strain. Reproduced withh permission from ref 267. Copyright 2012 American Chemical Society.

6.1.3. Strain Effect on Magnetism of Metallic Layered Transition Metal Dichalcogenides. Magnetism can be efficiently modulated by strain in m-LTMdCs materials.258,259 When the 2D materials become ultrathin, they are flexible and can be easily elongated. Figure 30a shows the effect of in-plane strain on magnetic moments per V atom (top panel) and per X atom (bottom panel) for monolayer 1T-VX2 from DFT calculations.250 Tensile strain enhances both magnetic moments, whereas compressive strain quenches the magnetic

moments. This modulation of magnetic moment with strain can be understood from the competition of ionic and covalent bonding interactions between V and X atoms. For example, when the tensile strain applied, the distance between V and X atoms become elongated, resulting in the reduction of covalent bonding interaction but enhancement of the ionic bonding interaction. Consequently, the enhanced ionic bonding interaction could lead to an increase in the population of unpaired electrons on V atom. 6322


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Figure 31. (a) Atomic structures and calculated isosurfaces of spin density for monolayer VS2 with sulfur vacancies (Vno, V1s, V2s, and V3s). Reproduced with permission from ref 271. Copyright 2016 Elsevier. (b) Atomic structures of pure, one side fully hydrogen passivated (1H) and both sides fully hydrogen passivated (2H) monolayer VX2. (c) Calculated energy difference between FM and AFM states of monolayer VX2 in terms of hydrogenation. Reproduced from ref 274. Copyright 2014 American Chemical Society. (d) Inverse field cooling magnetization curves of Cr1−xVxSe2 samples at a magnetic field of over 0.1 T. The inset shows Curie−Weiss fitting in the low temperature region. (e) FC and ZFC curves of Cr1−xTixSe2 samples at a magnetic field of over 0.1 T. Reproduced with permission from ref 278. Copyright 2013 American Physical Society.

enhances further with higher strain. As discussed, the tensile strain can reduce the covalent bonding and enhance the ionic bonding strength between Nb and X atoms. Accordingly, the enhanced ionic composition between atoms gives rise to unpaired electrons and consequently the magnetic moment can increase.265,266 Figures 30c,d show the magnetic moments of NbX2 (X = S and Se) on Nb and X atoms with the variation of strain.267 6.1.4. Doping Effect on Magnetism of Metallic Layered Transition Metal Dichalcogenides by Vacancy, Hydrogenation, and Substitution by Dopants. Doping or alloying has been used for modifying material properties such as carrier density, mechanical strength, and magnetism.268−270 There are three main approaches for doping of LTMdCs: vacancy creation, surface hydrogenation, and substitution by dopants. Chalcogen vacancies have a significant influence on magnetic properties in LTMdCs. The structural schematic and correlated isosurfaces of the spin density for four types of S vacancies (Vno, V1S, V2S, and V3S) are represented for monolayer VS2 in Figure 31a.271 The spin density of V atoms adjacent to S vacancy is redistributed. The magnetic moments of V atoms near the S vacancy are gradually increased with more S vacancies (1.17, 1.67, 2.32, and 2.74 μB for Vno, V1S, V2S, and V3S, respectively). The remaining electrons of the V atom adjacent to the S vacancy weaken the covalent bond between the V and S atoms to enhance the

Strain affects not only magnetic moment but also spin ordering. FM spin ordering state in VS2 monolayer is more stable than AFM state as the applied strain is modulated from compressive to tensile strain (Figure 30b); a similar trend is also observed in CrX2 system.250,260 This phenomenon of magnetic ordering can be well explained by combining the through-bond and through-space spin polarization models.261,262 The FM state in monolayer VS2 could originate from through-bond spin polarization, where an a atom can induce reverse spin on an adjacent b atom that is directly bonded to another a atom. For example, the up-spin of a V atom induces down-spin to S atom. As a consequence, the down-spin S atom again induces up-spin to another V atom, leading to long-range magnetic ordering. Because the magnetic moment of V atoms is greater than that of S atoms, the total magnetic moment is nonzero and leads to long-range FM ordering. Another magnetic ordering mechanism is the through-space model, where an a atom induces to reverse spin to an a atom without a mediation by a b atom. After all, the through-bond and through-space interactions result in FM and AFM state in magnetic materials, respectively. Another interesting phenomenon is that strain even induces magnetism to the nonmagnetic materials.263 NbX2 is a wellknown superconducting material, which has no magnetic ordering.264 When the tensile strain is applied to monolayer NbX2, a finite value of magnetic moment is generated, which 6323


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Figure 32. Schematic band structure of topological insulators (a) and Weyl semimetal (b) and their topological surface states. Fermi surface of type I (c) and type II (d) Weyl semimetals with dot and electron−hole pocket shapes, respectively. Reproduced with permission from ref 167. Copyright 2017 Annual Reviews.

alloying in the Cr−Se−Te system shows a tunable magnetic ordering. For example, AFM is stable in the Se-based compound, while FM is more favored in the Te-based compound.280−282

magnetic moment of the V atom. The S vacancy can also change the magnetic ordering. FM ordering is stable in pristine VS2 (no S vacancy) whereas AFM ordering is stable with the presence of S vacancies. Hydrogenation of 2D materials can modify their magnetism and induce FM from nonmagnetic materials.272,273 The hydrogenation of monolayer VX2 is also estimated by DFT calculations. Figure 31b shows the representative structures of pure monolayer VX2 and its one- (1H) and two-site (2H) hydrogen functionalization.274 The basic magnetic information is summarized in Figure 31c. Two interesting features are presented: (i) the exchange energy (Eex), where Eex = (EAFM − EFM), of monolayer VX2 increases as the composition is varied from S to Te, indicating a higher Curie temperature; (ii) the spin ordering and magnetic moment of VX2 are significantly affected by hydrogenation. In the case of 1H, VX2 loses its magnetic properties and further hydrogenation to 2H gives rise to AFM order in VX2. Hydrogen plays a role as an n-dopant to VX2, leading to the renormalization of the carrier density and electronic structure, which highly influences magnetism. The substitution of the transition metals is one of the promising methods to induce magnetism to nonmagnetic materials.275−277 CrSe2 has intrinsic AFM, and its magnetic ordering can be modified by V or Ti atom substitution.278 Figure 31d shows the inverse magnetization of Cr1−xVxSe2; the high-temperature behavior follows a Curie law. The sign of the Curie constant is changed from positive to negative, which indicates that the AFM is generated as the concentration of substituted V atoms increases. No noticeable change from Ti atom substitution was observed below 20%, while over 20% Ti substitution, the compounds displayed a FM behavior (Figure 31e). Ti substitution can elongate the lattice parameter a of Cr1−xTexSe2 alloys and favors ferromagnetic interaction, which is similar to the case of CrxTiyS2.279 Furthermore, chalcogen

6.2. Weyl Semimetal in 1Td WTe2 and MoTe2

As mentioned in section 4, there is a case where the two bands are crossed, known as band inversion.283−285 The name “band inversion” comes from the energy difference between the two energy bands changing from positive to negative in the momentum space. This phenomenon can generally happen in the band structure of solids. In such a case, the interesting physical concept of the topological band structure should be considered, especially when these bands are inverted due to the spin−orbit coupling (SOC) effect.167,171,283−285 Figure 32 shows the different behavior in the case of two bands intersecting each other. In quantum mechanics, such degeneracies (e.g., two states having the same energy at a certain k-point) should be not allowed due to the interaction between the two bands.170−172,286,287 This phenomenon is similar to that displays when bringing two similar atoms close together; their initial energy levels will split into two different energy levels. The consequence of the band−band interaction is the formation of an energy gap. This is the case of topological insulator, as shown in Figure 32a.167 However, there are several special cases, where two band-crossing points remain stable, as shown in Figure 32b.170,171 These points are called Weyl or Dirac points, depending on their degree of degeneracy, owing to the nature of the linear behavior of these bands near the crossing points.170−172 It is worth noting that the linear band dispersion in topological insulator originates from the surface state, while the 3D Weyl or Dirac points are truly bulk states. In contrast to the closed curve of the Fermi surfaces of the surface states in topological insulators, the 6324


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Figure 33. Band structure of 1Td-WTe2 with (b,c) and without SOC (a). The Weyl points are located approximately 50 meV above the Fermi level. The distance between two Weyl points is approximately 0.7% of the BZ width. Reprinted with permission from ref 289. Copyright 2015 Macmillan Publishers Ltd.

Figure 34. (a,d,g,h) Theoretical and (b,c,d,f) experimental band structure of 1Td-MoTe2. A good agreement between the theoretical and experimental results is observed. Reprinted with permission from ref 118. Copyright 2016 Macmillan Publishers Ltd.

Although the Weyl points exist, it should be located at or very near Fermi level and there should be no other state from other bands contributing to density of states at the Fermi surface,170 unless the physical properties of Weyl points are difficult to distinguish and be measured. Although a narrow band gap semiconductor without inversion symmetry is proposed as a good material to explore Weyl semimetals, there is no clear guideline for searching materials satisfying all above conditions.170 The existence of Weyl cones and Fermi arcs have been proved from two different classes of material: type I, TaAs family (e.g TaAs, TaP, NbAs, NbP) and type II, layered transition dichalcogennides, MoTe2.167 The WTe2, a sister material of MoTe2, is predicted to be type II Weyl semimetal, but the detection of the Weyl characteristics is more challenging due to the short distance between the two Weyl points.167,290−293 In this section, we focus on the band structure of 1Td WTe2 and MoTe2.

Fermi surfaces of the Weyl semimetals are arc type, which connects a pair of two Weyl points.286,288 There are two types of Weyl semimetal, based on the shape of the Weyl cone. Type I is representative for the Fermi surface shrinking to Weyl points. In contrast, type II of Weyl semimetals has tilting Weyl cones, giving rise to a Fermi surface consisting of both electron and hole carriers, as shown in Figure 32c,d.11,12,118,289 Type II Weyl semimetals can be viewed as inverted band structures of indirect semiconductors (Figure 8d). The searching guidelines for materials revealing Weyl semimetals are still unknown. However, there is a high possibility that the Weyl semimetal may exist in materials with no inversion or broken time reversal symmetry (e.g., magnetic materials).170,171 This condition is derived from the theoretical model based on the two-band system. In such conditions, the band is nondegenerate and the conditions for maintaining the Weyl cone can be satisfied more easily. This means that not all noninversion symmetry or magnetic materials will always have the Weyl cone. There is another important condition. 6325


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Figure 35. (a−d, i−l) Topological Fermi arcs in MoTe2 from simulation and (e−h) ARPES measurements at different energy levels. Reprinted with permission from ref 118. Copyright 2016 Macmillan Publishers Ltd.

Figure 33 shows the band structure of 1Td-WTe2 with (b,c) and without SOC (a) from the Σ to Γ points.289 The SOC is very strong in WTe2, indicated by a notable difference in the band structure with and without SOC. The small gap of cutting points is fully opened when the SOC is included. Interestingly, the Weyl points appear in the kz = 0 plane along the K−K′ direction, as shown in Figure 33c. However, these points are approximately 0.052 and 0.058 eV above the Fermi energy. Furthermore, the distance between the two Weyls point is too small (about 0.7% of the BZ width), leading to difficulties in the detection of these points due to the limitation of resolution in the ARPES measurements.292,293 To overcome this issue, the searching direction is being shifted toward MoTe2 and (W1−xMox)Te2 alloy.11,12,118,294,295 Figure 34 shows the theoretical and experimental band structures of MoTe2.118 The calculated band structure including the surface state is shown in Figure 34a. The bulk band structure is represented by the continuous spectrum due to the strong dispersion along the kz axis, while a sharp line indicates the surface state. The experimental ARPES is clearly consistent with the calculated band structure, except that the band is p-doped with the Fermi level is shifted down by 20 meV. To make clarification between the bulk and surface states, the band structures in Figures 34b,c is measured by pand s-polarized light, respectively. The surface state (marked as a black curve) and the bulk electron pocket (marked as blue) are clearly observed using the p-polarized light. The spectral function at the Fermi surface (e.g., the density of states at the Fermi surface) reveals a bell and bowtie shape for the electron

and hole pocket, respectively, as also observed in the ARPES results (Figure 34e,f). It is noticed that the Weyl points of MoTe2 are located at 5 and 45 meV above the Fermi level from theoretical calculation as shown in Figure 34g. One important feature of evidence for the Weyl semimetal is the existence of the Fermi arc (e.g., the topological surface state). While the arc can be clearly revealed in theoretical calculation, it is not easy to prove in experiments. In the case of MoTe2, the surface states are squeezed between the electron and hole pockets, which is difficult to be detected. An indirect way is to use theoretical calculation as a guideline to see how much consistency between the theoretical and experimental results, even with the iso-energetic surface. The evolution of the surface state at different energies is measured, as shown in Figure 35. Far from and below the Fermi level, the distance between the topological (red indicator) and trivial (gray indicator) surface state is increased and this is revealed in both the theoretical calculations and experimental results, indicating the topological arc state of the Weyl semimetal characteristic of MoTe2. An interesting property of the Weyl semimetal is the large unsaturated magnetoresistance. Both classes of Weyl semimetals reveal this characteristic.8,31,115,296,297 This originates from the coexistence of the electron and hole carriers, which is believed to be the main factor leading to the large magnetoresistance, similar to the case of the Bi crystal.166

7. SUMMARY AND PERSPECTIVES 2D materials have been synthesized in a form of bulk via flux method or CVT approaches, while monolayer or few-layer 2D 6326


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the superconductivity. Furthermore, the native of the atomic thickness can take more advantages. One typical example is the proximity effect, wherein the interaction between the 2D materials with the substrate will strongly affect to their properties. Whether this coupling effect can enhance or destroy the magnetism and superconductivity of the atomic thin layer is still unknown.

materials have been synthesized via typical CVDs. Unlike semiconducting components, mono- or few-layer metallic films are still in the infancy stage. They can be easily oxidized under ambient conditions or during synthesis, as already practiced in the monolayer 1T′-MoTe2,, making it difficult to generalize CVD approaches practiced during synthesis of semiconducting films. A special care is required to avoid such oxidation effects. Use of comprehensive air-free vacuum system combining various equipment such as material synthesis, characterization, device fabrication, and measurements is perhaps necessary. Phase engineering is also a big issue which has several challenges. A representative approach for transforming from semiconducting to metallic phase is chemical Li intercalation. Yet, this phase is not stable and evolves eventually to semiconducting phase. Another approach is the phase modulation of the atomic structure by physical approaches such as temperature, light irradiation, strain, and carrier injection. One may also take a route to atomic alloying process to overcome such problematic issues. For example, WS2 and WSe2 are typically known as H-phase materials, whereas the WTe2 is Td phase which is monoclinic structure. Tuning of the chalcogens contents in synthesis process (WS1−xTex or WSe1−xTex) will modulate electronic structures. The work should be further verified with some theoretical and experimental works. Challenges are in device applications, and one of the biggest issues is the achievement of ohmic contact. The phase transformation of semiconducting to metallic phase seems to be a shortcut to lower the contact resistance. Whether this approach is universal or not is still not clear because this strongly depends on the material. The use of h-BN layers between oxide layer and 2D layer or between metal electrode and 2D can reduce the Schottky barrier height but whether this achieves ohmic contact or not is still unknown. Using graphene as an intermediate contact material is a promising method to reduce the contact resistance, as previously reported.298−300 Because the interaction between 2D materials and electrode metal is quite weak, functionalization of the 2D materials on the contact area prior to electrode metal deposition is also a possible approach to improve the contact resistance. Graphene is a good candidate for future transparent electrode. While the conductivity of m-LTMdCs may not match with that of graphene, some 2D m-LTMdCs has strong anisotropy which reveals orientation-dependent optical and electrical properties. Frequency dependent conductivity in particular at low frequency limit is interesting for RF devices. While 1Td WTe2 and MoTe2 are proved to be the Weyl semimetal, the Weyl points are located above the Fermi energy. This prevents to directly characterize the properties of the Weyl points by the electrical transport measurements. Therefore, a good strategy of doping should be developed to move the Fermi energy reach to the Weyl points. This work should involve both first-principle calculations and experimental measurements. Searching for rich classes of 2D materials for Weyl semimetal is another open research area. Many efforts have been spent for searching high temperature superconductivity in the m-LTMdCs. Most m-LTMdCs follow the BCS theory. This requires a high energy phonon, which is strongly coupled with electrons to form electron pairs. However, the formation of the PLD phase indicates the softened phonons that have phonons with a quite low energy. It gives rise to low Tc. Nevertheless, the m-LTMdCs are still a platform for verifying the validation of the theory applied for

AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. ORCID

Dinh Loc Duong: 0000-0002-4118-9589 Young Hee Lee: 0000-0001-7403-8157 Author Contributions ∥

Gang Hee Han and Dinh Loc Duong contributed equally to this work.

Notes

The authors declare no competing financial interest. Biographies Gang Hee Han received his Ph.D. from the Department of Physics in Sungkyunkwan University in 2011 under the supervision of Prof. Young Hee Lee. He joined the Department of Astronomy and Physics in the University of Pennsylvania (UPenn) in the United States as a postdoctoral position between 2012 and 2014. He is now a research professor of IBS Center for Integrated Nanostructure Physics (CINAP) from 2014 in Sungkyunkwan University (SKKU). His research has focused on the synthesis of low dimensional materials such as carbon nanotubes, graphene, hexagonal boron nitrides, and layered transition metal dichalcogenides. Dinh Loc Duong received his Ph.D. from the Sungkyunkwan Institute of Nanoscience and Nanotechnology (SAINT) in 2012 under the supervision Prof. Young Hee Lee. After his first postdoc in the same lab from 2012 to 2014, he joined the Max-Planck-Institute for Solid State research in Kern’s department from 2014 to 2016 as a junior scientist. He is now research professor at the IBS Center for Integrated Nanostructure Physics (CINAP), Sungkyunkwan University (SKKU). His current research interests are 2D materials, including their growth, characterization, and applications. Dong Hoon Keum entered Uiduk University in 2007 as an undergraduate. He received his B.S. degree from Yeungnam University. In 2011, he joined the Department of Energy Science, Sungkyunkwan University, as a Ph.D. candidate. His current research interests focus on the synthesis of two-dimensional materials and their applications. Seok Joon Yun entered Sungkyunkwan University in 2006 as an undergraduate and graduated in 2012. In 2012, he got into the Department of Energy Science, Sungkyunkwan University as a Ph.D. candidate student under the supervision Prof. Young Hee Lee. He has been working on the synthesis of 2D materials such as graphene, hexagonal-boron nitride, black phosphorus, and transition metal dichalcogenides. Prof. Young Hee Lee has been a full professor of the Physics Department at SKKU, since 2001. He received his Ph.D. from Kent State University in Ohio (1986) in Physics. Prior to joining SKKU in 2001, Prof. Lee was a full professor in the Physics Department at Chonbuk National University since 1986. He was a visiting scholar at Ames Laboratory, Iowa State University, in 1989, IBM, Zurich, in 6327


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1993, and Michigan State University in 1996. Currently, he is the Director of the Center for Integrated Nanostructure Physics, Institute for Basic Science, at SKKU. He serves for an Associate Editor of European Physics Letters, Energy Storage Materials, and ACS Nano. He was awarded the first SKKU fellow in 2004 at SKKU, science award from Korean Physical Society in 2005, Lee Hsun Research Award, IMR, Chinese Academy of Sciences, China, in 2007, and Presidential Award in Science and Education in 2008, Eistein Award from Chinese Academy of Sciences. He was also nominated as a National Scholar by Ministry of Education in 2006 and has been a fellow of Korean Academy of Science and Technology since 2007. He recently got Sudang prize. His work has focused on understanding the fundamental properties of nanostructures in 0D, 1D, 2D, and their hybrid heterostructures, design and synthesis of various heterostructures to implement unique physical and chemical properties. His research covers carrier dynamics, carrier multiplication phenomena, hot carrier solar cell, thermoelectrics, quantum mechanical tunneling phenomena, and 2D soft electronics. He has published more than 500 scientific papers in international journals and his total citation number exceeds over 35000 times with an H-index of 84 (Google Scholar).

ACKNOWLEDGMENTS This work was supported by the Institute for Basic Science of Korea (IBS-R011-D1). ABBREVIATIONS USED 2D two-dimensional LTMdCs layered transition metal dichalcogenides s-LTMdCs semiconducting LTMdCs m-LTMdCs metallic LTMdCs CDW charge density wave CVD chemical vapor deposition CVT chemical vapor transport MBE molecular-beam epitaxy ARPES angle-resolved photoemission spectroscopy MFCVD metal film chemical vapor deposition MOxCVD metal-oxide chemical vapor deposition MHCVD metal-halide chemical vapor deposition MOCVD metal−organic chemical vapor deposition HCVD hybrid chemical vapor deposition LSCVD liquid source chemical vapor deposition PLD periodic lattice distortion TEM transmission electron microscope STM scanning tunneling microscope C&IC&NC commensurate and incommensurate and nearly commensurate BCS Bardeen−Cooper−Schrieffer FM & AFM ferromagnet and antiferromagnet SOC spin−orbit coupling REFERENCES (1) Geim, A. K.; Novoselov, K. S. The Rise of Graphene. Nat. Mater. 2007, 6, 183−191. (2) Dean, C. R.; Young, A. F.; Meric, I.; Lee, C.; Wang, L.; Sorgenfrei, S.; Watanabe, K.; Taniguchi, T.; Kim, P.; Shepard, K. L.; et al. Boron Nitride Substrates for High-Quality Graphene Electronics. Nat. Nanotechnol. 2010, 5, 722−726. (3) Li, L.; Yu, Y.; Ye, G. J.; Ge, Q.; Ou, X.; Wu, H.; Feng, D.; Chen, X. H.; Zhang, Y. Black Phosphorus Field-Effect Transistors. Nat. Nanotechnol. 2014, 9, 372−377. (4) Mannix, A. J.; Zhou, X.-F.; Kiraly, B.; Wood, J. D.; Alducin, D.; Myers, B. D.; Liu, X.; Fisher, B. L.; Santiago, U.; Guest, J. R.; et al. 6328


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