Two-Dimensional Topological Insulators: Progress and Prospects

Perspective pubs.acs.org/JPCL

Two-Dimensional Topological Insulators: Progress and Prospects Liangzhi Kou,*,† Yandong Ma,‡ Ziqi Sun,† Thomas Heine,‡ and Changfeng Chen§ †

School of Chemistry, Physics and Mechanical Engineering Faculty, Queensland University of Technology, Garden Point Campus, QLD 4001, Brisbane, Australia ‡ Wilhelm-Ostwald-Institut für Physikalische und Theoretische Chemie, Universität Leipzig, Linnéstraße 2, 04103 Leipzig, Germany § Department of Physics and Astronomy and High Pressure Science and Engineering Center, University of Nevada, Las Vegas, Nevada 89154, United States ABSTRACT: Two-dimensional topological insulators (2D TIs) are a remarkable class of atomically thin layered materials that exhibit unique symmetry-protected helical metallic edge states with an insulating interior. Recent years have seen a tremendous surge in research of this intriguing new state of quantum matter. In this Perspective, we summarize major milestones and the most significant progress in the latest developments of material discovery and property characterization in 2D TI research. We categorize the large number and rich variety of theoretically proposed 2D TIs based on the distinct mechanisms of topological phase transitions, and we systematically analyze and compare their structural, chemical, and physical characteristics. We assess the current status and challenges of experimental synthesis and potential device applications of 2D TIs and discuss prospects of exciting new opportunities for future research and development of this fascinating class of materials.

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condition, which is achievable in specially equipped laboratory settings, imposes severe limitations for practical device applications. A possible alternative is to find materials with intrinsic strong magnetic fields to induce QHE. In 1988, Haldane theoretically proposed a toy model5 in 2D honeycomb-lattice system in an alternating magnetic field with zero net flux. This model was considered at the time as a pure theoretical exercise for conceptual demonstration without a viable pathway toward practical implementation. There were at least two major obstacles. One is the difficulty in generating the required alternating magnetic field inside the material, and the other is the generally believed instability of any long-range order in 2D materials driven by long-wavelength fluctuations.6 In recent decades, significant developments in 2D material synthesis and characterization have paved the way for renewed exploration leading to discoveries of topological states that confirm and expand the realm of understanding of novel physical phenomena in this fascinating class of materials. The successful fabrication of graphene,7 a single atomic layer of honeycomb carbon lattice, has provided an ideal platform to demonstrate and explore Haldane’s theoretical model, and it also has raised hope of achieving the QHE in 2D materials. Kane and Mele pointed out8 that the intrinsic spin−orbit coupling (SOC) in graphene can be regarded as an alternating magnetic flux introduced in the Haldane model,5 which makes graphene the first real material system that may realize the theoretically proposed new topological state. It was found that

he 2016 Nobel Prize in Physics has been awarded to David J. Thouless, F. Duncan M. Haldane, and J. Michael Kosterlitz “for theoretical discoveries of topological phase transitions and topological phases of matter.” In 1972, Kosterlitz and Thouless identified a new type of phase transition in two-dimensional (2D) systems, where topological defects are found to play a crucial role in driving the so-called Kosterlitz−Thouless phase transition.1,2 This theory is crucial to understanding intriguing quantum phenomena at very low temperatures in select types of magnets and superconducting and superfluid films. In 1982, the concepts of topological description were used by Thouless and co-workers to explain the quantization of the Hall conductance in 2D electron gases, giving rise to a key characteristic known as Thouless− Kohmoto−Nightingale−Nijs (TKNN) number.3 Under a strong external magnetic field,4 the Landau-level quantization and quantum Hall effect (QHE) are induced, which are manifested by a vanishing longitudinal conductance but nonzero quantized Hall conductance, leading to an intriguing state of insulating bulk but metallic edge. The amplitude of the quantized Hall conductance is in units of e2/h and found to relate to the TKNN/Chern number, which is topologically invariant as long as the bulk band gap remains open, reflecting the topological nature of QHE, i.e., the Hall conductance is quantized at constant values. As a result, the metallic edge state is robust against weak disorder like nonmagnetic defects. These ground-breaking discoveries introduced novel physics principles and established a solid foundation for understanding a new type of topologically driven phase transitions in 2D materials. The Landau-level quantization and associated QHE can be achieved only in strong magnetic fields, and this stringent © 2017 American Chemical Society

Received: January 28, 2017 Accepted: April 10, 2017 Published: April 10, 2017 1905

DOI: 10.1021/acs.jpclett.7b00222 J. Phys. Chem. Lett. 2017, 8, 1905−1919

The Journal of Physical Chemistry Letters

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Figure 1. Energy bands for a 1D zigzag graphene strip in the (a) QSH phase λv = 0.1t and (b) the insulating phase λv = 0.4t. In both cases λSO = 0.06t and λR = 0.05t. The edge states on a given edge cross at ka = π. The inset shows the phase diagram as a function of λv and λR for 0 < λSO< t. (c) Schematic diagrams showing two-terminal and four-terminal measurement geometries. Panels a and b reprinted with permission from ref 9. Copyright 2005 American Physical Society. Panel c reprinted with permission from ref 8. Copyright 2005 American Physical Society.

the thickness exceeds the critical value, the valence band top from the 6s orbit with Γ6 symmetry (odd parity) from Hg is inverted above the conduction band bottom from the p orbit with Γ8 symmetry (even parity), leading to a 2D TI state with a single pair of helical edge states. The critical thickness is calculated to be around 6.3 nm, while the topologically protected edge state can be obtained by solving the BHZ model equation with an open boundary condition (Figure 2c). It has been shown that although the mechanics of the BHZ model is different from that of the Kane−Mele model, the resulting outcome is the same, namely, all the QSH insulators have an energy gap in the 2D bulk, but with metallic edge states bridging the bulk gap, and two sets of edge states with opposite spin polarization counter-propagate on the boundary. The BHZ mechanism is confirmed by later calculations based on continuum models, as well as more realistic first-principles and tight-binding (TB) methods, which all produced the QSH state and the topological phase transition. Different from the extremely small gap (10−3 meV) in graphene,10 which was used as the primary system in the Kane−Mele model, the QSH state and topologically nontrivial gap (10 meV) in HgTe/CdTe QWs are large enough for direct experimental verification.15 For thin QWs with width d < 6.3 nm, the insulating regime showed the conventional behavior of vanishingly small conductance at low temperature; on the other hand, for thicker quantum wells (d > 6.3 nm), the nominally insulating regime showed a plateau of residual conductance close to 2e2/h (Figure 2d). This residual conductance is independent of the sample width, indicating that it is caused by edge states. These observations provide experimental evidence for the presence of the QSH effect. Of the two approaches to generating 2D TIs, the Kane−Mele model8 based on graphene is closely tied to the original toy model proposed by Haldane,5 where a bulk band gap is opened by SOC at two inequivalent Dirac points and can be generalized to other honeycomb-lattice structures with two sublattices. Meanwhile, the BHZ model15 proposes to induce a band inversion by SOC in a 2D semiconductor. These distinct theoretical approaches point to two general routes for realizing 2D TIs, that is, by opening up a band gap in 2D Dirac semimetals or by inducing a band inversion in narrow-gap semiconductors. We classify the former as type I 2D TIs, while the latter are classifed as type II, and present below characterization and discussion of 2D TIs in these two general categories. It is noted that the theoretical background and mechanisms on the fundamental physics of 2D TIs have been extensively

the SOC opens a small bulk gap at the Dirac point in the electronic band structure of graphene, converting the system from a gapless semimetal to a gapped state. This SOC driven state possesses an electronic structure containing a gapped interior and novel gapless edge states that counter-propagate at the boundaries with opposite spins (see Figure 1), resulting in a vanishing charge Hall conductance but nonzero quantum spin Hall (QSH) conductance. This new phenomenon is termed the QSH effect with the electronic spin as the quantum number and characterized by the Z2 topological order.9 Such a spin helical metallic edge state inside a bulk gap is robust against weak disorder because of the protection of the time-reversal symmetry. All electron scatterings by nonmagnetic impurities are forbidden, leading to dissipationless transport edge channels. Such QSH insulators driven by topological phase transitions described by the Haldane mechanism are called topological insulators (TIs). Graphene is the first predicted 2D TI to possess QSH effect; however, this intriguing effect has eluded direct experimental detection because the bulk energy gap of graphene is extremely small (10−3 meV)10 because of its weak SOC. A large increase of the SOC effect is therefore crucial to fundamental exploration and potential application of graphene-based QSH insulators. Subsequent studies11 have proposed to enhance the SOC in graphene by heavy adatom doping or placing it on substrate materials with strong SOC interactions. Meanwhile, considerable progress also has been achieved by exploring other honeycomb lattice materials (low-buckled graphene-like materials) with stronger SOC effects, such as silicene,12 gemanene, and stanene.13 Parallel to the development of the Kane−Mele model, Bernevig, Hughes, and Zhang (BHZ) proposed in 200614 a more general mechanism for generating TIs, namely, through an electronic band inversion, where the usual ordering of the conduction and valence band with different parities is “inverted” by the relativistic effects (or the inert pair effect in chemical sense). This mechanism does not require the honeycomb-lattice system and alternating magnetic flux as in the original Haldane model,5 therefore allowing the presence of 2D TI states in a much larger variety of materials with strong SOC, and this new formulizm has served as the template for further developments of many 2D TI materials. As an early case study, it was predicted that HgTe/CdTe quantum wells (QWs) are TIs resulting from a quantum phase transition as the thickness of HgTe is tuned. As shown in Figure 2a,b, when the film thickness is below a critical value, the system is a conventional insulator, but when 1906



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Figure 2. (a) Energy band dispersions of HgTe and CdTe near the Γ point. The CdTe/HgTe QW in the normal regime E1 > H1 with d < dc (left lower panel) and in the inverted regime E1 < H1with d > dc (right lower panel). (b) Energy variation of E1 and H1 bands versus QW thickness d. Lower panels are energy dispersion relations of the E1 and H1 subbands at thickness of 40, 63.5, and 70 Å (from left to right), respectively, and the band inversion between E1 and H1 can be seen beyond the critical thickness. (c) Crossing field (red triangles) and energy gap, Eg (blue open dots), as a function of QW width d resulting from an eight-band k·p calculation. (d) The longitudinal four-terminal resistance of various normal (d = 5.5 nm) and inverted (d = 7.3 nm) QW structures as a function of the gate voltage measured for B = 0 T at T = 30 mK. Panels a and b reprinted with permission from ref 14. Copyright 2006 AAAS. Panels c and d reprinted with permission from ref 15. Copyright 2007 AAAS.

experimental synthesis. We examine key properties and performance characteristics essential to potential device applications and comment on current efforts and future directions of research on this fascinating class of materials. It should be noted that the rapid progress in theoretical prediction of 2D TIs has considerably outpaced experimental synthesis efforts, and the discussions below refer to theoretical results unless otherwise noted. Graphene is a prototypical type I 2D TI proposed as the original Kane−Mele model system.8 Although its nontrivial band gap is too small for direct experimental observation,10 the conceptual breakthrough of identifying a new state of matter by an assessment of topological properties of the electronic band structure has opened an important new field of research. The graphene-based TI model has been generalized to a large

These distinct theoretical approaches point to two general routes for realizing 2D TIs, that is, by opening up a band gap in 2D Dirac semimetals or by inducing a band inversion in narrow-gap semiconductors. discussed in several recent reviews.16,17 In this Perspective we focus primarily on the latest progress in the identification and synthesis of a large number of new 2D TI materials. We present a systematic categorization and characterization of such 2D TIs and discuss the status and challenges of their 1907



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Figure 3. (a) Adatoms on graphene. Depending on the element, adatoms favor either the high-symmetry “bridge” (B), “hollow” (H), or “top” (T) position in the graphene sheet. (b) The panels correspond to the band structure and LDOS computed using DFT without and with spin−orbit coupling, as well as results from the tight-binding model. With thallium adsorption, a gap of 21 meV opens at the Dirac points. Reprinted with permission from ref 11. Copyright 2001 American Physical Society.

family of 2D materials with honeycomb lattices,12 and considerable progress along this direction has been achieved, especially the efforts to enhance the nontrivial band gap via defect or substrate doping of graphene and the investigation of many graphene analogue systems, which we examine below. The extremely weak SOC in carbon produces an almost vanishingly small nontrivial gap in graphene, and finding an effective approach to enhancing the SOC strength holds the key to elevating the gap that protects the QSH state. There have been concerted efforts in recent years to achieve this goal. An early proposal is to use heavy and magnetic adatom doping on graphene surface, and the idea is that these adatoms would play the role of mediating both intrinsic and Rashba spin−orbit coupling via electron transfer or proximity effect.18,19 However, local magnetic moments induced by the adatoms may destroy the time reversal symmetry needed to protect the QSH state in the system, which could lead to a new phenomenon called quantum anomalous Hall (QAH) effect.20 One of the important preconditions to induce a significant QSH state in graphene is that the adatom-induced impurity band should be far from the Fermi level so that the π band from graphene is not substantially altered. Through tight-binding and first-principle analyses, Weeks et al.11 found that two heavy elements, indium and thallium, are capable of stabilizing a robust QSH state in graphene, producing nontrivial gaps several orders of magnitude higher than that of the pristine graphene, up to 7 and 21 meV, respectively, at the coverage of 6%, as indicated in Figure 3. These predictions revived graphene as a viable candidate system for observing the QSH effect with the associated nontrivial band gap on the order of 100 K or higher. It is worth noting that the reported results are based on calculations using a periodic supercell of graphene with indium and thallium atoms uniformly distributed at each hexagonal center of the honeycomb lattice. Later experiments found, however, that the metal adatoms tend to form clusters, rather than distribute uniformly on graphene surface. Further investigation indicates that a random distribution of adatoms weakens the intervalley scattering but has only limited influence on other key quantities such as SOC. As a result, the QSH state can be stabilized in the presence of randomly distributed adatoms,21 and this theoretical prediction has been confirmed by experiments,22 where the QSH effect in chemically functionalized graphene with enhanced SOC remains robust in the presence of adatom clustering. Because of the inevitable significant electron transfer caused by heavy atom adsorption, graphene is always heavily electron-doped, which significantly shifts the Dirac cone into the valence band as shown in

Figure 3b, and this situation is undesirable for electronic device applications. Yang et al.23 proposed a kinetic pathway from first-principles calculations to realize a high-temperature QSH insulator by n−p codoping of graphene, which moves the Dirac cone close to the Fermi level. Most importantly, a large intrinsic band gap of 26.9 meV is generated when graphene is codoped by thallium and tetrafluorotetracyanoquinodimethane (F4-TCNQ). This study provides a solution for experimental studies and practical applications of the high-temperature QSH effect. It also has been predicted that various 3d, 4d, and 5d metal atoms can introduce large SOC to graphene.24,25 For example, it is shown that Ru adatom may induce a nontrivial topological phase in graphene due to an intervalley interaction.26 Depending on the Ru adatom concentration, graphene can exhibit different topological phases, such as metallic, QSH, QAH, or trivial insulating state. The feasibility of the proposed theoretical strategies has been verified by recent experiments. For instance, graphene with iridium nanocluster decoration has been shown to possess SOC enhancement,27 and the spin relaxation time measurement indicates a sizable Kane−Mele-like coupling strength of over 5.5 meV. An angle-resolved photoemission spectroscopy measurement28 showed that intercalation of a Pb layer between a graphene sheet and the Pt(111) surface leads to the formation of a gap of about 200 meV, and spin-resolved measurements also confirmed the band splitting to be of a spin−orbit nature with the measured near-gap spin structure resembling that of the QSH state in graphene, as proposed by Kane and Mele.8 When the band structure is tuned, graphene acquires functionalities beyond its intrinsic properties and becomes more attractive for possible spintronic applications. Achieving significant SOC enhancement in graphene is not limited to heavy adatom doping. Some light elements can also remarkably enhance the SOC and drive graphene into a more pronounced QSH phase. Castro Neto and Guinea18 have shown that an impurity-induced sp3 distortion renders SOC in graphene comparable to those in some zinc-blende semiconductors. This result points to another feasible approach to increasing the SOC in graphene, thus paving the way for finding versatile graphene-based QSH systems. Heavy adatom adsorption or decoration is an effective approach to enhancing the nontrivial band gap and the QSH state in graphene; however, the accompanying electron transfer and interaction between adatoms and graphene considerably shift the Dirac cone away from the Fermi level, thus introducing large doping effects,11,24,26,28 which are undesirable for device applications. Meanwhile, the metallic states introduced by the dopants tend to hybridize with the π state of graphene and 1908



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Figure 4. (a) Structural model of the BiTeI/graphene QW. (b) Calculated band structures of the BiTeI/graph QW (left to right panels) with the SOC but without the coupling between the graphene and BiTeI layers, without the SOC but with the interlayer coupling, and with both the SOC and interlayer coupling, respectively. The red (blue) dots represent the contributions from graphene (BiTeI). (c) The MoTe2/graphene QW structure. The total energies as a function of relative positions are shown at the right. The obtained electronic band structures without and with SOC are shown in panel d. The band inversion process is illustrated in the panels below. Panels a and b reprinted from ref 34. Copyright 2014 American Chemical Society. Panels c and d reprinted with permission from ref 29 Copyright 2015 Elsevier.

top of Sb2Te3 can also be significantly increased by the proximity effect, driving the system into the QSH phase with a TI gap of 20 meV. It is interesting to note that the Rashba effect and vertical electric field induced by the structural asymmetry in the graphene−Sb2Te3 heterostructure also makes a substantial contribution to the opening of the large nontrivial gap. It is noted, however, that this greatly enhanced gap is still not sufficiently robust against thermal disturbances of the ambient environment. This problem is addressed by a recent work on graphene sandwiched by BiTeX (X = Br, Cl, I) layers, which themselves are not TIs but possess strong SOC and Rashba effects.33 Theoretical calculations show34 that the van der Waals heterostructures of BiTeX/Graphene QWs (Te atoms are located at the hexagonal center of graphene) can form a family of Z2 TIs with nontrivial gaps up to 70 meV, which can be increased to 120 meV under pressure, see Figure 4a,b, and such large gaps are sufficient to maintain the QSH state for roomtemperature applications. These theoretical predictions have been supported by recent experiments,35,36 in which an artificial interface between monolayer graphene and few-layer semiconducting tungsten disulfide (WS2) was created. The measurements show that in such structural setups graphene acquires a SOC as high as 17 meV, which is 3 orders of magnitude higher than the value in intrinsic graphene. This result is achieved without modifying any of the structural properties of the graphene layer,36 and the obtained value is close to the theoretical predictions. In the heterostructures presented above, the Dirac cone of graphene is not affected because the electronic states from the cladding layers are far from the Fermi level; the role of the cladding layers is to increase the SOC, which, in turn, enhances the gap. It should be mentioned that compared to the

destroy the Dirac cone. To avoid these situations, weak interactions and proper band alignments between graphene and doping elements need to be ensured. A promising way to avoid the strong hybridization is to utilize systems with weak van der Waals interactions, which can enhance the SOC and induce the QSH state in graphene through interface interactions. Firstprinciples calculations show that the SOC and associated TI energy gap in graphene can have a giant (3 orders of magnitude) proximity-induced enhancement, to the level of millielectronvolts, which can be further increased to the order of 10 meV under pressure, when the graphene layer is sandwiched between thin slabs of Sb2Te3, rendering the QSH effect observable by experiments.29 The Dirac cone states of graphene at the K and K′ points are folded into the Γ point because of the √3 × √3 supercell structure, but these states are unaffected by the band states from the cladding layers. Distinct from the situation with heavy metal adatom adsorbed graphene systems,11,24,26,28 the Dirac cone in the sandwiched heterostructure remains at the Fermi level without any shift into either the conduction or the valence band. Because the underlying physics of the graphene heterostructure stems from the proximity enhanced SOC, the results depend on the interlayer distance and SOC strength of the cladding layers, but they are insensitive to other material and fabrication details such as the stacking order and lattice mismatch. This makes it easy to generalize this approach, and similar phenomena are also observed in sandwiched heterostructures in which graphene is placed between transition-metal dicholcogenides.30,31 An example can be seen in Figure 4, which shows the results for graphene sandwiched between MoTe2. The sandwiched structure is actually not a prerequisite for achieving the proximity-driven topological phase; Jin and Jhi32 predicted from first-principles calculations that the SOC of graphene on 1909



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silicene on metal substrates like Ir, Cu, Mg, Au, Pt, and Al substrates,46 and found that the Dirac cone of silicene will be destroyed regardless of the substrates but can be preserved by intercalating alkali metal atoms between silicene and the metal substrates. This finding raises hope for observing QSH in such systems. The situation for gemanene is similar, although it has been synthesized and characterized on Au(111),46,47 Al(111),48 and platinum (111)49 surfaces; Si substrate;50 and Ge2Pt clusters.51 The reconstructed atomically thin sheets induced by the interaction with the substrate are prone to losing the massless Dirac fermion character and the associated unique physical properties of freestanding germanene. Few-layer epitaxial germanene on Au substrate was shown to possess Dirac cones due to reduced interaction,46 making it possible to observe QSH in germanene. Moving downward in the periodic table from carbon, silicon, and germanium, one would find elements like Sn and Pb, which hold great promise for achieving the QSH state because of their much stronger intrinsic SOC. Theoretical studies indicate that the Sn single layer (also called stanene13) is structurally stable in the honeycomb lattice but with low-buckled configurations due to the overlap between the π and σ orbitals that stabilize the system. Electronic structure calculations show that two energy bands cross linearly at the K point in the absence of the SOC, indicating that the Dirac cone is located at the K point; a band gap up to 100 meV opens up when the SOC is switched on. These results suggest that stanene is a viable candidate for being a QSH insulator. Because the graphene analogue of lead (the heaviest group IV element) is a metal, the nontrivial gap of 100 meV in stanene is the largest among possible group IV element-based 2D TIs. Subsequent experiments have synthesized stanene and confirmed its TI phase.52 In addition, 2D layered structures of group V elements in honeycomb lattices may also host QSH states, as recently predicted in a bismuth bilayer.53 Another example is the Sb layered structure; while it is not an intrinsic TI, the Sb film can be driven into a topological phase by moderate applied strains.54 Chemical functionalization of 2D materials is a powerful tool for creating new materials with desirable features, as demonstrated in graphane55 and fluorinated graphene.56 The great flexibility in the selection of the chemical functional group enables formation of a series of chemically new materials. This concept is also useful for designing new QSH insulators. For example, a single-layer germanene without functionalization is a QSH insulator with a nontrivial gap of 23.4 meV, but a functionalized GeI layer becomes a 2D TI with a much enhanced gap of about 0.3 eV after the passivation with iodine. Further calculations indicate that a series of GeX (X = H, F, Cl, Br, and CH3)57,58 layered compounds are trivial insulators, but they can be transformed into TI phases with sizable nontrivial gaps under moderate tensile strains. In these systems, the σ orbitals with stronger SOC interactions dominate the states around the Fermi level after the functionalization, which replace the original π orbitals with much weaker SOC interaction and thus enhance the gaps. The coupling of the px,y orbitals of Ge and heavy halogens in forming the σ orbitals also plays a key role in the further enlargement of the gaps in halogenated germanene systems. This mechanism is quite generally applicable and can be also applied to Sn, Pb, Bi, Sb, and even As layered structures although a few of them are trivial large-gap semiconductors before they are functionalized. For example, fluorinated stanene is predicted to host the QSH state with a

previously discussed proximity-enhanced SOC effect, a different mechanism for gap opening is at work here. Because of the different parities of the valence band from graphene and the conduction band from Bi, the inversion between the bands of the cladding layer and the π band of the graphene layer turns Bi2Se3/graphene QW into a Z2 TI with a nontrivial gap of 30−50 meV. This phenomenon can be generalized to systems with other cladding layers like Bi2TeSe2 or Bi2Te2Se. It has been shown by experiment that smooth graphene/Bi2Se3 interfaces can be fabricated;37 it is therefore feasible to realize the Bi2Se3/graphene QWs with current experimental techniques to verify the predicted QSH state. In the Haldane model, two conditions are required for realizing the QSH state, namely, a 2D honeycomb lattice and an alternating magnetic field with zero net flux. The rapid recent progress in 2D material prediction and synthesis38 has led to the identification of several 2D TIs beyond graphene. One such graphene-analogue system is silicene, which is the graphene equivalent of silicon, which possesses the hexagonal structure with two sublattices and buckling in the freestanding configuration, and it is, like graphene, an excellent 2D material platform to realize the Haldane model. Although silicene is less stable than graphene, the successful synthesis of epitaxial silicene sheets on a silver (111) substrate39 provides a good foundation for investigating its novel physics. Because of the larger atomic number and associated stronger SOC in silicon atom compared to carbon atom, silicene has been theoretically shown12 to be a viable Z2 TI with topologically nontrivial electronic structures and QSH effect, and the SOC-driven band gap is 1.55 meV, which, although still quite small, is much higher than that of pristine graphene, and the gap can be increased to 2.9 meV under certain stress conditions. Similar to the graphene QWs, calculations suggested that encapsulated silicene QWs between transition-metal dichalconides (TMDC) layers can increase the nontrivial gap to over 100 meV.39,40 Meanwhile, the 2D germanium layer, known as germanene, with a similar low-buckled stable structure is also predicted to exhibit a SOC driven gap of 23.9 meV, which is large enough for direct experimental observation in the low-temperature regime.12 Although theoretical predictions suggest promising prospects of QSH effect in these graphene analogue TIs, there remain major obstacles for their experimental realization, including the weak structural stability, high surface chemical activity, and small band gaps. Different from the flat lattice of graphene, silicene and gemanene possess buckled structures because of the weakened π−π orbital overlaps. According to the doublebond rule, elements like Si and Ge with 3p or 4p orbitals cannot form stable double bonds, and their structural stabilities rely on properly chosen functional groups or substrates. Most reported silicene syntheses used Ag substrates,39,41,42 and the strong electron transfer and hybridization between silicene and the substrate severely alter the Dirac cone, rendering the QSH effect unobservable. There were also some reports about successful synthesis of silicene on ZrB243 and Ir substrates,44 but the intrinsic properties of silicene in these cases are also altered. A possible solution is offered by a recently developed method, in which the synthesized silicene on Ag is transferred onto an insulating Al2O3 base with the intrinsic property of silicene preserved.45 This process requires a high-vacuum environment, and extremely low temperatures are also required to observe the QSH state with a nontrivial gap of 1.55 meV. Recent theoretical simulations proposed epitaxial growth of 1910



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nontrivial gap of 0.3 eV,13 and functionalized arsenene (AsX, X = F, OH, and CH3) is a 2D TI with a gap of 0.1−0.16 eV.59 Most surprisingly, the nontrivial gap values can reach the record high level of around 1 eV for the two heaviest metals Pb and Bi when their layered structures are functionalized with CH360 or H, halogen.61,60,62 Such a large nontrivial gap and robust helical edge states are more than enough for room-temperature applications. However, synthesizing and stabilizing these structures remains a big experimental challenge; useful insights may be gained from past successes, such as the chemical functionalization of graphene.63

semiconductor.64 The strong SOC in the transition-metal atoms combined with the lack of structural inversion symmetry generate a giant spin splitting of 148−456 meV according to first-principles calculations.65 The strong intrinsic SOC in MX2 provides the key ingredient for hosting the QSH state, but the large band gap separating the bottom of the conduction band and the top of the valence band impedes the band inversion. Recent theoretical investigations66 indicate that in a structurally distorted phase (1T′), see Figure 5a,b, an intrinsic band inversion between chalcogenide-p and metal-d bands can occur, and the SOC opens a nontrivial gap up to 0.1 eV. This gap is tunable by applied strain and switchable by a vertical electric field. Different from the hexagonally packed atoms with Bernal (ABA) stacking in 2H phase, the 1T′ structure is formed with a spontaneous period-doubling 2 × 1 lattice distortion of the ABC stacked 1T phase (Figure 5a). Phonon calculations indicate that all the 1T′ MX2 are dynamically stable, but their synthesis remains an outstanding challenge. It is known that the 2H phase of MoS2 or WS2 can be transformed into the 1T phase via alkali metal intercalation67,68 or by e-beam irradiation,69 and distorted (2a × a) 1T phases consisting of zigzag chains (WTe2-like structures) have been observed. Although such distorted 1T phases may be regarded as 1T′ phases mentioned above, this assignment still requires direct experimental evidence. As a result, the presence of the QSH state in the 1T′ phase of MX2 needs further investigation. Subsequently, other phases of TMDCs are also predicted to possess QSH state with large nontrivial gaps. For example, by a theoretical particle swarm structure search, a new T″ phase of MoS2, which can be regarded as a structural combination of 2H and 1T′ phase, has been identified; electronic calculations

Chemical functionalization of 2D materials is a powerful tool for creating new materials with desirable features. Compared with type I 2D TIs designed following the Kane−Mele model, 2D TIs based on the BHZ mechanism of band inversion and parities exchange at time-reversal symmetry points are even more diverse and abundant. The structures of such type II 2D TIs are not limited to the honeycomb lattice as proposed in the Haldane model. The key idea of the BHZ model is the inversion of bands with different parities, which provides guidance for the search for such materials. Transition-metal dichalcogenide (TMDC) MX2 (M = Mo, W; X = S, Se) monolayer is a direct gap semiconductor. It has a triatomic layer structural arrangement with the metal atom layer sandwiched between the chalcogenide atom layers. As the layer thickness increases, the system turns into an indirect gap

Figure 5. (a) Atomistic structures of monolayer 1T′ transition-metal dichalcogenides MX2. (b) Band structure and edge density of states of 1T′-MoS2. (c) Top and side view of the 2D organometallic superlattice. Dashed lines show the unit cell, and the two metal atoms are labeled 1 and 2. l and h are the distance and height difference between the two metal atoms, respectively. (d) Band structures of triphenyl-lead (TL) lattice without and with spin−orbit coupling (SOC). The dashed line indicates the Fermi level. The zoomed-in band structures around the Dirac point are also shown. Panels a and b reprinted with permission from ref 66. Copyright 2014 AAAS. Panels c and d reprinted with permission from ref 76. Copyright 2013 Nature Publishing Group. 1911



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hydrogenated diamond-like GaBi bilayer is shown to possess a large nontrivial band gap of 0.302 eV.83 The recently discovered84,85 2D transition-metal carbides M2C, the so-called MXenes, are layered materials that can be exfoliated from the bulk materials. However, different from the direct mechanical exfoliation of graphene peeled off from bulk graphite, MXenes need to be first processed with wet chemical method to remove the A layer (A is usually a group IIIA to IVA element) with toxic HF from MAX phase.86 MXenes have shown great potential for a variety of applications ranging from electrodes in supercapacitors and batteries to sensors and reinforcements in polymers. Their outmost surfaces are terminated with the transition metals, and this makes these materials strongly chemical active and easily oxidized. Most interestingly, functionalized MXenes with oxygen M2CO2 (M = W, Mo and Cr) form a new family of 2D TIs. Different from the most common s−p orbit exchange mechanism, the band inversion in this family of materials, which is crucial to producing the nontrivial band topology, is found to occur among the bonding and antibonding states of M d orbitals. The predicted nontrivial gap is up to 0.194 eV from GGA calculations, which is corrected to 0.472 eV with hybrid functional HSE.87 The MXene family is not limited to the M2C structure, and it can be expanded as new members with ordered double transition metals M′2M″C2 (M′=Mo, W; M″=Ti, Zr, Hf).88,89 After oxidation, the topological phases are well-preserved in these newly added members, M′2M″C2O2, with gap values in the range of 0.041−0.285 eV (GGA), which are corrected to 0.12−0.41 eV (HSE). While surface oxidation helps to stabilize the structures, surface functionalization is not a necessary condition to achieve the QSH state in these transition-metal carbides. Recently, another family of compounds MC (M = Ti, Zr, Hf)90 has been demonstrated to be 2D TIs without any surface passivation. Similar to the carbides, transition-metal halides are also theoretically shown to be TIs driven by the large SOC in these metal atoms; examples include MX (M = Zr, Hf; X = Cl, Br, and I)91 with gaps of 0.12−0.4 eV and TaCX (X = Cl, Br, and I) with gaps of 0.23−0.36 eV.92 Although various MXenes have been fabricated experimentally and extensively studied theoretically as discussed above, finding any topological phases in the family of structures is currently still at the theoretical prediction stage. It is highly promising and expected to stimulate experimental efforts and progress in the near future. A key ingredient for producing TIs is a strong SOC from either a constituent material component or from external sources such as doping or proximity effect; there is in principle no restriction on the specific material form, which means the QSH state also can be realized in organic materials. Following this idea, covalent organic frameworks (COFs) containing heavy metal atoms like Pb and Bi have been shown to be organic 2D TIs. First-principles calculations predicted a family of organic 2D TIs in organometallic lattices, Pb(C6H5)3 and Bi(C6H5)3 (Figure 5c). Designed by assembling molecular building blocks of triphenyl-metal compounds with strong SOC into a hexagonal lattice, these new organic TIs exhibit nontrivial topological edge states robust against significant lattice strain.76 Additional organometallic framework compounds, Ni3C12S12 (gap value, 13.6 meV)93 consisting of π-conjugated nickel-bisdithiolene, 2D indium-phenylene organometallic framework (IPOF),94 and Cu−dicyanoanthracene (DCA) lattice,93 were all shown to exhibit nontrivial topological states. The identification of these organic TIs greatly broadens the scientific and

indicate that this new phase exhibits QSH effect with a nontrivial gap of 0.42 eV.70 A class of stable hexagonal 2D TMDC allotropes of MX2 (M = Mo, W; X = S, Se, Te) comprising 4- and 12-membered rings are identified to be 2D TIs with large band gaps ranging from 41 to 198 meV.71 It is also predicted that square transition-metal dichalcogenides MX2 (M = Mo, W;X = S, Se, Te) show sizable intrinsic nontrivial band gaps ranging from 24 to 187 meV.72−74 Besides the MX2 family, other layered materials like M2Te (MCu, Ag)75 also have been predicted to host the QSH state. While these proposed TMDC phases have been shown to be structurally, thermally, and dynamically stable, and some are even predicted to be more stable than the corresponding hexagonal phases, their synthesis remains a technical challenge, requiring further investigation and experimental progress. The element Bi possesses a strong SOC of around 1 eV, which suggests that compounds containing Bi may be promising TI candidates. Theoretical calculations indicate that binary compositions of group III elements (B, Al, Ga, In, and Tl) and Bi in a buckled honeycomb structure are potential candidates for being 2D TIs.77 Band inversions are identified in pristine GaBi, InBi, and TlBi bilayers with gaps as large as 560 meV due to the relatively weakly localized electrons in these compounds induced by a small electronegativity difference between the two elements, making these materials suitable for roomtemperature applications. Meanwhile, although BBi and AlBi are not intrinsic 2D TIs, topological phase transitions could be induced by ∼6.6% strain. Strain engineering even drives the semiconductor GaAs film into a topological phase, opening a nontrivial gap up to 275 meV.78 Subsequently, the same idea has been applied to more binary III−V compounds in 2D buckled honeycomb lattice structures,79 and possible 2D TIs are screened from 75 binary combinations of group III (B, Al, Ga, In, and Tl) and group V (N, P, As, Sb, and Bi) elements.80 A total of six compounds (GaBi, InBi, TlBi, TlAs, TlSb, and TlN) are identified to possess topologically nontrivial band gap. All these hexagonal compounds were proposed theoretically without checking for thermal and dynamical stability by phonon and molecular dynamics simulations, which raises questions about their structural stability. In the cubic or tetragonal structures, each atom X (Ga, In, Tl) bonds with four neighboring Bi atoms, while in the proposed hexagonal structure, each atom X bonds with only three Bi atoms. Surface passivation or substrates are possible ways to stabilize these structures. Simulations indicate that under hydrogenation, four of them (GaBi, InBi, TlBi, and TiN) remain topologically nontrivial, and the largest band gap reaches 855 meV. With surface passivation by halogen atoms, a Dirac cone from the p orbits of III/Bi atoms is formed at the Γ point in the absence of SOC, resulting in very large nontrivial band gaps up to 0.6−1 eV for X2−III−Bi monolayers (X = F, Cl, Br, I).62 Due to the structural asymmetry of these III−V compounds, the induced Rashba effect also plays a significant role in determining the physical properties.77,81 Furthermore, topologically nontrivial phases also have been predicted in ternary III−V chalcogenides in rhombohedral phases TlBiTe2, TlBiSe2, and TlSbX2 (X = Te, Se, S), which are all identified to have topologically nontrivial gap with a single Dirac cone on certain surface terminations.82 While these predictions still await experimental confirmation, calculations have proposed that Si(111) substrate is an idea platform to support the growth of these 2D TIs.78 Besides the graphene-like structures, some other stable III−V structural phases are also predicted to host the QSH state. For example, 1912



Perspective

systems. Besides the HgTe QWs, semiconductor QWs InAs/GaSb/AlSb were also proposed to exhibit an “inverted” phase and QSH state.109 The theoretical model and findings are confirmed by experimental studies of low-temperature electronic transport in inverted InAs/GaSb composite QWs, where the conductance as a function of sample length and width is measured to show strong evidence for the existence of helical edge modes.110 Among the first systems predicted to be a 2D TI is the bilayers of bismuth due to the strong SOC effect,111 and direct evidence from experiments112 came in 2014, when onedimensional topological edge states of bismuth bilayer were decoupled from the states of the bulk Bi substrate and directly measured with scanning tunnelling microscopy. Moreover, the remarkable coherent current propagation along the edge is shown to be consistent with the strong suppression of backscattering as predicted for the propagating topological edge states. When the bismuth bilayer is fabricated on the Sb nanofilms, its topological electronic properties are shown to be tunable by the quantum confinement effect.113 Following the synthesis of graphene, several other ultrathin layered materials based on group-IV elements, like silicene39 and germanene,47 have been experimentally synthesized on Ag surface by MBE and mechanical exfoliation. These systems have been theoretically proposed to be 2D TIs,12 but they have yet to be experimentally confirmed because of their chemically active surface and small nontrivial gaps, as well as the strong chemical bonding with the substrate that destroys the intrinsic electronic properties of silicene or germanene. More recently, Zhu et al.52 reported successful fabrication of 2D Sn monolayer, or stanene, on Bi2Te3 (111) surface by MBE, which has been confirmed by atomic and electronic characterization using scanning tunnelling microscopy and angle-resolved photoemission spectroscopy, see Figure 6a−c, in conjunction with first-principles calculations. The measured electronic properties of stanene are comparable with the theoretical predictions, thus providing compelling evidence for its 2D TI phase. Further experimental investigations are still required to verify other predicted properties such as a very large nontrivial bandgap and the enhanced thermoelectric performance. More direct observations of 2D TI behaviors have been realized in ZrTe5,96 where the nontrivial gap of 100 meV and constant density of states within the entire gap at the monolayer step edge have been demonstrated by combining scanning tunnelling microscopy and spectroscopy and angle-resolved photoemission spectroscopy (Figure 6d,e). These features are well reproduced by the first-principles calculations, which point to the topologically nontriviali nature of the edge states in these systems. A major challenge in experimental synthesis of 2D TIs is finding fabrication methods that can produce high-quality samples suitable for characterization. Chemical approaches, like MBE, are effective in preparing 2D materials, but it is hard to obtain large-size, high-purity specimens, and the synthesis process often requires stringent conditions. Taking stanene and bismuth bilayer as examples, their chemically active surfaces make the structures unstable in the ambient environment, thus requiring high vacuum conditions for synthesis and characterization. Strong coupling to the states of the substrates leads to a finite density of states (DOS) within the gap in the area away from the edges, which makes measurements of the QSH effect and device applications nearly infeasible. Meanwhile, because the interactions in the corresponding bulk structures of many of these materials are dominated by strong covalent bonding, it is impossible to obtain their 2D layers using the mechanical

technological scope and impact of TI research and potential applications. When Bi or Pd atoms are replaced with magnetic elements (e.g., Mn), spontaneous magnetization combined with spin−orbit coupling gives rise to a quantized Hall conductivity, and the broken time-reversal symmetry by Mn leads to a family of 2D organic TIs for realizing the QAH effect.95 Despite its prominent role in producing the band inversion and associated QSH state, SOC is not a fundamental prerequisite for generating the new state of quantum matter in topological phases. One example is the 2D TI material ZrTe5/HfTe5,96,97 where the band inversion is not driven by SOC. Its valence and conduction bands meet at the Fermi level, and the SOC simply opens up a topologically trivial band gap without an induced band inversion. Instead, the obtained band inversion is due to the band splitting caused by the nonsymmorphic features of the space group of the material. The same mechanism is also seen in transition-metal halide MX (M = Zr, Hf; X = Cl, Br, and I)91 monolayers and square transition-metal dichalcogenides MX2.72−74 The already large 2D TI family is fast evolving with new members being added at a high rate. Some recently predicted examples include the BiF buckled square lattice,98 tetragonal bismuth bilayer,99 SnX2 (X = S, Se, or Te) with pentagonal rings,100 silicon-based chalcogenide,101 functionalized TlSb monolayers,102 and so on; all of them have been theoretically predicted to be thermally and dynamically stable from phonon frequency and molecule dynamics simulations. These findings not only enrich the 2D TI family but also reveal diverse and interesting structural, physical, and chemical characteristics that can be harnessed for innovative applications. Meanwhile, it should be noted that in addition to the 2D TIs due to timereversal symmetry, there is another class of TIs driven by crystalline symmetry, and these so-called topological crystalline insulators (TCIs)103 include different material families like TlSe and TlS monolayers104 and SnTe material class.105,106 In this Perspective, we focus on time-reversal symmetry-based TIs and refer the readers to a recent review107 for further discussion of TCIs.

In contrast to the flourishing and fast developments on the theoretical front as outlined above, the progress has been much slower in the experimental synthesis and measurements of 2D TIs. In contrast to the flourishing and fast developments on the theoretical front as outlined above, the progress has been much slower in the experimental synthesis and measurements of 2D TIs. The first experimentally demonstrated 2D TI is the HgTe/CdTe QW realized in 2007 by molecular-beam epitaxy (MBE),15 where the critical QW thickness for the topological quantum phase transition is measured to be around 6.3 nm and the quantized Hall conductance of 2e2/h is observed (Figure 2c,d). However, its small nontrivial gap of 10 meV renders this early prototype 2D TI useful only for laboratory demonstration but impractical for actual applications. Even so, the ensuing developments based on the study of the HgTe QWs not only led to the findings of 3D TIs like the Bi2Se3 family108 but also inspired the search for 2D TIs in additional 1913



Perspective

Figure 6. (a) Atomic structure model for the 2D stanene on Bi2Te3(111). (b) ARPES spectra of stanene on Bi2Te3 along the K−Γ−K direction. (c) ARPES spectra along the Γ−M−Γ−K−M−K directions. Blue dotted lines mark the experimental electronic bands of stanene. Green dashed lines mark one of the hole bands of Bi2Te3(111). (d) STM constant current topographic image of the cleaved (010) surface of ZrTe5 crystal. (e) Band dispersions along Γ−X measured at 24 K. Panels a−c reprinted with permission from ref 52. Copyright 2015 Nature Publishing Group. Panels d and e reprinted with permission from ref 96. Copyright 2016 American Physical Society.

by selective surface chemical functionalization,13 see Figure 7, where the left part of the specimen is in a TI phase after being passivated with F while the right part is passivated with hydrogen and remains a normal insulator, and in this arrangement the helical metallic edge state exists and propagates along the interface line, which serves as a dissipationless conducting channel. As the topological phase and QSH effect can be modulated by a vertical applied electric field,66,116 see Figure 7b, it provides flexibility in controlling the topological phase and associated performance characteristics for device applications. This feature points to the possibility of an all-electrical control of the on/off spin conductance of helical edge states, which has significant implications for QSH-based devices.117 Based on the theoretical prediction of 1T′ MX2 as 2D TIs and their electric switch capability, Qian and co-workers proposed52 a topological field effect transistor (TFET) by constructing vdW heterostructures of 2D MX2 and 2D wide-gap insulators. The proposed device is sketched in Figure 7c, where the top and bottom gates supply the vertical electric field to control the on/off function (Figure 7d). 2D wide-gap insulators such as hexagonal boron nitride electrically insulate adjacent QSH layers, hence protecting the parallel helical edge channels from being gapped by interlayer hybridization. The device supports dissipationless charge/spin transport in the “on” state (Z2 = 1) with a quantized conductance. A moderate electric field can switch 1T′-MX2 to an ordinary insulator (Z2 = 0) and turn the edge conduction off. This proposed vdW-TFET possesses important technical advantages, because the operation mechanism is fundamentally different from the traditional metal-oxide-semiconductor FETs. The idea of TI-based transistors is also proposed118 based on experimental progress of Mn- and Se-doped Bi2Te3,119 although further direct experimental demonstration is still required. These proposals provide crucial platforms for realizing lowdissipation devices in quantum electronics and spintronics. Meanwhile, 2D TIs are also suggested to play an important role in topological quantum computation schemes120,121 because of the existence of Majorana fermions when the TI material comes in contact with a superconductor. Moreover, pure and protected metallic edge states imply possible and promising

exfoliation method that has been used to obtain graphene from bulk graphite. Similar issues further impede the functionalization of these layers, like TMX (TM = Bi, Pb, Sb, Sn, As, Si, Ge; X = H, F, Cl, Br, I, OH, CH3, ...).13,100 In addition to the challenges regarding the fabrication and characterization of pristine 2D layered materials as indicated above, it is often even harder to realize precise functionalization, which is important to achieving stable structural configurations for the observation of the QSH state in using either top-down or bottom-up methods.63,55 Ongoing developments of theoretical findings and experimental techniques are expected to address these challenges. In particular, discovery of new 2D TI materials with desirable structural arrangements may help resolve some key issues and move the research forward. For example, recent firstprinciples calculations predicted114 that 2D SiTe is a TI with a large nontrivial gap of 220 meV; most interestingly, this layered material has been synthesized as a constituent component of a three-dimensional superlattice,115 where the interlayer interaction is dominated by weak van der Waals forces, thus offering the possibility of mechanical exfoliation. Impeded by the hitherto slow progress of experimental synthesis and characterization of 2D TIs, their demonstrated device applications have been so far quite limited. Only a few applications are theoretically proposed, still awaiting experimental verification. Nevertheless, the prospects of using 2D TI materials in innovative device design and fabrication are highly promising based on their outstanding properties. A unique feature of 2D TIs is their helical gapless edge states inside a bulk energy gap, which is spin-locked because of the protection of the time-reversal symmetry, namely, the propagation directions of the edge electrons are robustly linked to specific corresponding spin orientations. Accordingly, all the scatterings of electrons in the presence of nonmagnetic impurities are forbidden, leading to dissipationless transport edge channels. This exceptional property is perfectly suited for many device applications in nanoelectronics and spintronics. Examples include dissipationless conducting “wires” for nanoelectronic circuits, which could significantly lower power consumption and heat generation rates, a key requirement for advanced integrated circuits. This idea is illustrated in the case of stanene 1914



Perspective

Figure 7. (a) Schematic diagram showing helical edge states at the phase boundary between the TI and trivial insulator by different chemical functional groups passivation. The helical edge states can be patterned by controlling the chemical functionalization and used as dissipationless conducting “wires” for electronic circuits. (b) Vertical electric field induced a topological phase transition. Shown are calculations for monolayer 1T′-MoS2 under different electric fields. The first and second rows show the bulk band structure and edge density of states, respectively. (c) Schematic of vdW-TFET. The central component (d) is a vdW heterostructure of alternating monolayer 1T′-MX2 and mono/multilayer widegap insulators. Panel a reprinted with permission from ref 13. Copyright 2013 American Physical Society. Panels b−d reprinted with permission from ref 66. Copyright 2014 AAAS.

applications in chemical catalysis,122 as well as the possibilities to build novel Dirac devices34 with dissipationless transport channels. These promising prospects for innovative nanodevice design and fabrication offer important guidance for further development of next-generation electronics and spintronics, which is still at an early stage of exploration and discovery of fundamental principles and effective synthesis, processing, and characterization techniques. As an emergent and unique member in the low-dimensional materials family, 2D TIs have attracted great attention from the physics, chemistry, and materials science research communities. The fundamental physics of this new phenomenon has been captured by the Kane−Mele and Bernevig−Hughes−Zhang models, which have introduced essential working mechanisms for generating a new state of quantum matter with topologically nontrivial electronic structures, i.e., the QSH state. Guided by such fundamental understanding, a large number and rich variety of 2D TIs have been theoretically proposed, and some have been experimentally synthesized and characterized. Theoretical explorations of 2D TIs have revealed many interesting possibilities to construct the novel QSH state in a diverse range of material systems, including different material groups, configurations, and functionalization schemes. Some of

these systems exhibit intrinsic QSH state, while others are driven by applied electric field or strain, and most can be tuned by one or more external controls like electric and/or strain fields. These predicted 2D TIs have exhibited a rich variety of operating mechanisms for the topological phase transitions in specific materials, ranging from intrinsic SOC, proximity SOC, internal hybridization of electronic states, externally induced band shift and hybridization, and so on. Such extensive theoretical knowledge is a tremendous asset in understanding the QSH effect in 2D materials and in the search for additional material systems that possess this novel property. Theoretical studies of 2D TIs remain an extremely active current research field with many opportunities for further exploration and elucidation of material specific mechanisms, which may lead to the discovery of additional 2D TIs in new material types, forms, and configurations and under various external conditions. Experimental synthesis and characterization of 2D TIs remain a major challenge at present, offering outstanding opportunities for innovation and breakthrough. The realization of the QSH state in 2D TIs requires fabrication of high-quality samples that can be obtained under relatively easy and robust synthesis conditions and that are suitable for further characterization and eventual device implementation. While some techniques are 1915



Perspective

Prof. Thomas Heine graduated from TU Dresden (Germany) and, after postdoctoral stages in Bologna (Italy), Exeter (UK), and Dresden, became Associate (2008) and Full (2011) Professor of Theoretical Physics/Theoretical Materials Science at Jacobs University Bremen (Germany). In 2015 he accepted the appointment as the Chair of Theoretical Chemistry at Leipzig University (Germany). His research interests include the development of methods and software for materials science, molecular framework compounds, 2D inorganic materials, and theoretical spectroscopy.

Experimental synthesis and characterization of 2D TIs remain a major challenge at present, offering outstanding opportunities for innovation and breakthrough.

Prof. Changfeng Chen received his Ph.D. from Peking University in 1987. After postdoctoral appointments at UC Berkeley and University of Oregon, he joined University of Nevada, Las Vegas, where he is now a Professor of Physics. His current research interests include material properties under extreme stress, pressure, and/or temperature conditions; new structural forms and novel phenomena in nanoscale materials; and strongly correlated electron systems.

capable of producing 2D TIs, they suffer major drawbacks that impede their practical applications; examples include the MBE technique that is too expensive and stringent for practical production purposes and mechanical exfoliation that is limited in its ability to obtain large-scale, high-quality samples. More promising are perhaps some chemical approaches that are capable of growing large quantities of high-quality samples. Also useful would be the identification of new 2D TIs in quasi-layered materials that can be readily separated and transferred into freestanding film form or onto appropriate substrates. Progress in these areas has been made, but more work is needed for further advancement. The discovery of the novel topological state in 2D TIs has spurred tremendous interest in recent years. While the fundamental physics principles and material requirements are generally understood, much remains to be explored, especially effective and robust synthesis techniques and innovative device design and demonstration. This interdisciplinary field is expected to experience continued fast growth and offer ample research opportunities for the foreseeable future.

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ACKNOWLEDGMENTS Financial support by the ARC Discovery Early Career Researcher Award (DE150101854) is gratefully acknowledged. C.F.C. was partially supported by the U.S. Department of Energy through the Cooperative Agreement DE-NA0001982.

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REFERENCES

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Liangzhi Kou: 0000-0002-3978-117X Thomas Heine: 0000-0003-2379-6251 Notes

The authors declare no competing financial interest. Biographies Dr. Liangzhi Kou received his Ph.D. in 2011 from Nanjing University of Aeronautics and Astronautics. He was an Alexander von Humboldt Fellow at the Bremen Center of Computational Materials Sciences (BCCMS) in Germany during 2012−2014 and a Research Associate at UNSW Australia in 2014. He has been a Lecturer at Queensland University of Technology under an ARC-DECRA fellowship since 2015. His research mainly focuses on computational discovery and design of novel 2D materials for energy applications and 2D topological insulators. Dr. Yandong Ma completed his Ph.D. under the supervision of Prof. Ying Dai at Shandong University in 2014. He is currently a postdoctoral fellow in Prof. Thomas Heine’s group. His research interest mainly includes theoretical characterization of low-dimensional nanomaterials. Dr. Ziqi Sun received his Ph.D. degree from Institute of Metal Research, Chinese Academy of Sciences in 2009. After a one-year postdoctoral fellowship at the National Institute for Materials Science, Japan, he joined the University of Wollongong, Australia with funding from an ARC-APD fellowship (2010), a UOW VC fellowship (2013), and an ARC-DECRA fellowship (2015). He is currently a Senior Lecturer at Queensland University of Technology, Australia. His research interest includes metal oxide nanomaterials and bioinspired inorganic nanomaterials for sustainable energy applications. 1916



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Two-Dimensional Topological Insulators: Progress and Prospects

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