Enhanced Valley Splitting of Transition-Metal Dichalcogenide by

Research Article Cite This: ACS Appl. Mater. Interfaces 2019, 11, 18858−18864

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Enhanced Valley Splitting of Transition-Metal Dichalcogenide by Vacancies in Robust Ferromagnetic Insulating Chromium Trihalides Changqing Lin,† Yiran Li,† Qilin Wei,† Qian Shen,*,† Yingchun Cheng,*,† and Wei Huang†,‡ †

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Key Laboratory of Flexible Electronics & Institute of Advanced Materials, Jiangsu National Synergetic Innovation Center for Advanced Materials, Nanjing Tech University, 30 South Puzhu Road, Nanjing 211816, China ‡ Shaanxi Institute of Flexible Electronics (SIFE), Northwestern Polytechnical University (NPU), 127 West Youyi Road, Xi’an, 710072 Shaanxi, China ABSTRACT: Recently, single-layer CrI3, a member of the chromium trihalides CrX3 (where X = Cl, Br, or I), has been exfoliated and experimentally demonstrated as an atomically thin material suitable for twodimensional spintronics. Valley splitting due to the magnetic proximity effect has been demonstrated in a WSe2/CrI3 van der Waals heterojunction. However, the understanding of the mechanisms behind the favorable performance of CrI3 is still limited. Here, we systematically study the carrier mobility and the intrinsic point defects in CrX3 and assess their influence on valley splitting in WSe2/CrI3 by first-principles calculations. The flat-band nature induces extremely large carrier mass and ultralow carrier mobility. In addition, intrinsic point defectslocalized states in the middle of the band gapshow deep transition energy levels and act as carrier recombination centers, further lowering the carrier mobility. Moreover, vacancies in CrI3 can enhance ferromagnetism and valley splitting in a WSe2/CrI3 heterojunction, proving that chromium trihalides are excellent ferromagnetic insulators for spintronic and valleytronic applications. KEYWORDS: valley splitting, CrI3, transition metal dichalcogenide, point defect, ferromagnetism

1. INTRODUCTION

affect valley splitting in TMDs remains unknown and deserves investigation. In this work, we have investigated the carrier mobility of CrX3 and explored the influence of the intrinsic point defects on the electronic properties of CrX3 and on the valley splitting of a WSe2/CrI3 heterojunction by first-principles calculations. The band edges of CrX3 are flat, inducing large carrier mass and low mobility. The formation energies of intrinsic point defects in CrX3 are large, indicating a low concentration. Some point defects, such as Cr-vacancy (VCr), I-vacancy (VI), and Iinterstitial (iI), have relatively low formation energies, which induces deep level states and further reduces electron mobility. Therefore, CrX3 is a robust ferromagnetic insulator. VCr and VI can significantly improve the valley splitting of the WSe2/CrI3 van der Waals heterojunction by interlayer interaction enhancement. For defect engineering, we can create vacancies by electron or ion irradiation to enhance the ferromagnetism of CrI3. We demonstrate robust ferromagnetism of insulating chromium trihalides against point defects, showing great potential for spintronic and valleytronic applications.

1

Since the discovery of graphene in 2004, two-dimensional (2D) materials have attracted significant attention because of their broad applications in ultrathin electronic, spintronic, and optoelectronic devices. Many other 2D materials have been extensively studied, such as h-BN,2 transitional-metal dichalcogenides (TMDs),3 and MXene.4 Because single-layer TMDs have spin−valley coupling, they are considered to be a promising 2D material for spintronics and valleytronics.5−8 The magnetic proximity effect is theoretically proposed9,10 and experimentally demonstrated on an EuO substrate11 to control the spin and valley in TMDs. Since 2017, single-layer chromium trihalides, CrX3 (where X = Cl, Br, or I),12−14 Fe3GeTe2,15 and Cr2Ge2Te616 have been experimentally synthesized and verified as 2D ferromagnetic materials. CrX3 has been used in 2D spintronic devices, showing excellent performance.15,17 Multilayer CrI3 has been used as a magnetic substrate to promote valley splitting in TMDs such as WSe218 because of the proximity effect.19−22 Though the research development of CrX3 is fast, there are still some arguments about the fundamental properties of CrX3. For example, some researchers regard CrX3 as an insulator,12,14 while others classify it as a semiconductor.13,23,24 Defects can have significant influence on the properties of semiconductors, insulators, and magnetic materials. As a novel family of ferromagnetic materials, studies about the defect influence, such as the effect of point defects to the magnetism, for CrX3 are very limited.24 Moreover, how defects in CrX3 can © 2019 American Chemical Society

2. CALCULATION METHOD First-principles calculations based on density functional theory were performed using the plane-wave pseudopotential method, which is implemented in the QUANTUM-ESPRESSO code.25 Received: March 18, 2019 Accepted: April 30, 2019 Published: April 30, 2019 18858

DOI: 10.1021/acsami.9b04843 ACS Appl. Mater. Interfaces 2019, 11, 18858−18864

Research Article

ACS Applied Materials & Interfaces

point and conduction band minimum (CBM) is at the Γ point in the first Brillouin zone. The band edges are very flat, indicating large carrier mass. By taking the second-order partial differential of the energy band near VBM and CBM, we obtain the effective mass of holes (mh) and electrons (me). The carrier mobility can be evaluated by using the deformation potential

The generalized gradient approximation26 with Perdew− Burke−Ernzerhof (PBE) parameterization27 for the exchange and correlation functional was used.Ultra-soft pseudopotentials were utilized for elements Cr, Cl, Br, and I. A kinetic energy cutoff of 544 eV and a Monkhorst−Pack k-mesh of 4 × 4 × 1 were set. The energy convergence threshold ion optimization was 2.72 × 10−3 eV. The vacuum was set to 20 Å for singlelayer CrX3 to prevent interaction between images of slab models. The in-plane lattice parameters of WSe2 and CrI3 are 3.32 and 6.85 Å, respectively. A 4 × 4 supercell was used for WSe2 and a 2 × 2 was used for CrI3 to build the WSe2/CrI3 van der Waals heterostructure with 3.3% lattice mismatch. To calculate the band structure of WSe2/CrI3, the spin−orbit coupling effect was taken into account.

approximation with formula28 μ2D =

2eℏ3C 2D 3kBT |m*|2 E12

, where m* is

the effective mass, T is the temperature, E1 is the deformation potential constant, which represents the shift of the band edges (VBM for holes and CBM for electrons) induced by the strain, and C2D is the elastic modulus of the 2D system, C2D = [∂2E/ ∂δ2]/S0, where E is the total energy of the supercell, δ is the applied uniaxial strain, and S0 is the area of the optimized supercell. The effective mass and mobility of CrX3 are shown in Table 1. For CrCl3, CrBr3, or CrI3, the effective masses of the hole

3. RESULTS AND DISCUSSION 3.1. Structure. The unit cell of single-layer CrX3 is a honeycomb lattice where Cr atoms are sandwiched between two atomic planes of X, as shown in Figure 1. The unit cell of

Table 1. Properties of CrX3: Band Gap Eg, Electron and Hole Effective Masses me and mh, Electron Mobility μe, and Hole Mobility μha Eg/eV me/m0 mh/m0 μe/cm2/V s μh/cm2/V s

CrCl3

CrBr3

CrI3

MoS2b

MoS2c

MoS2d

1.70 6.02 5.33 0.02 0.05

1.49 3.76 3.47 4.41 5.63

1.44 26.92 7.16 0.11 0.64

1.64a 0.48a 0.60a 53.78a 119.55a

1.64 0.48 0.60 60.32 152.18

1.57 0.48 0.57

a c

Parameters of MoS2 are also listed for comparison. bPresent work. Reference 28. dReference 29.

are always smaller than those of the electrons and the mobilities of holes are higher, indicating that holes are more favorable to be driven by an electric field. We take a typical 2D semiconductor, MoS2, for comparison. The effective masses of electrons and holes of single-layer MoS2 are 0.48 and 0.60m0, respectively, which is consistent with previous reports.28,29 The effective masses of electrons or holes of three kinds of CrX3 are greater than 3.00 m0, which is greater than those of MoS2. Of all three kinds of CrX3, CrI3 has the largest me and mh. Because of the large effective masses, the carrier mobilities are rather small. The mobilities of holes/electrons are 0.02/0.05, 4.41/ 5.63, and 0.11/0.64 cm2/V s for CrCl3, CrBr3, and CrI3, respectively. The carrier mobilities of CrX3 are 2−3 orders smaller than those of MoS2 (119.55/53.78 cm2/V s). Therefore, chromium trihalides are more like an insulator than a semiconductor as claimed.13,23,24 CrI3 is the bestperforming of the three kinds of CrX3. 3.3. Region of Chemical Potential for CrX3 Growth. For crystal growth, it is important to control the elemental chemical potentials. From a database search, we have obtained all binary compounds containing Cr and X, CrX2, and CrX3.30 The chemical potentials of Cr and X should obey the equation ΔμCr + 3ΔμX = ΔHf(CrX3) to form CrX3. Δμi, which equals μi − μsolid , expresses the relative chemical potential referenced to i the chemical potential of its elemental solid (μsolid ). For i simplicity, we labeled Δμi as the chemical potential of element i in our manuscript. To avoid the formation of elemental crystals of Cr, Cl2, Br2, and I2 in the process of growth, the conditions of ΔμCr < 0 and ΔμX2 < 0 should be satisfied. Meanwhile, in order to prevent the synthesis of CrX2, the ΔμCr + 2ΔμX < ΔHf(CrX2) constraint also needs to be satisfied. The stable chemical potential regions for CrCl3, CrBr3, and CrI3

Figure 1. (a) Unit cell and (b) Brillouin zone of single-layer CrX3. (c) 3 × 3 × 1 supercell CrX3 model with 72 atoms.

CrX3 contains eight atoms as shown in Figure 1a. The in-plane lattice parameters of CrCl3, CrBr3, and CrI3 are 6.07, 6.39, and 6.86 Å, respectively. To simulate point defects, we first constructed a 3 × 3 × 1 supercell containing 72 atoms. Then, a series of intrinsic point defects were created, including two vacancies (VCr and VX), two interstitials (iCr and iX), and two substitutions (CrX and XCr). All the defect-containing supercells are optimized to the ground state. 3.2. Effective Mass and Carrier Mobility. Figure 2a−c shows the band structures of single-layer CrCl3, CrBr3, and CrI3. All band structures show indirect band gaps, which are 1.70, 1.49, and 1.44 eV for CrCl3, CrBr3, and CrI3, respectively. The valence band maximum (VBM) of CrX3 is found at the M

Figure 2. Band structures of (a) CrCl3, (b) CrBr3, and (c) CrI3. 18859


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Figure 3. Calculated stable chemical potential ranges for (a) CrCl3, (b) CrBr3, and (c) CrI3. The purple area surrounded by points A, C, and D.

Figure 4. Calculated defect formation energies as a function of the Fermi level for various intrinsic point defects in (a−c) CrCl3, (d−f) CrBr3, and (g−i) CrI3 under different conditions: (a,d,g) Cr-rich (point A), (b,e,h) Cr-moderate (point B), and (c,f,i) Cr-poor (point C).

The formation energy of a defect α ionized to the charge state q is defined as ΔHf(α,q) = E(α,q) − E(perfect) − ∑iniΔμi + q(EF + EVBM), where the formation energy ΔHf(α,q) is a function of both the electron Fermi energy EF and the chemical potential Δμi of the species i involved in the defects. (α, q) represents the total energy of the supercell with defect α in the charge state q. The total energy of the perfect crystal supercell is defined as (perfect), and ni represents the number of atoms i added (ni > 0) or removed (ni < 0). The energy of VBM EVBM is taken as a reference to determine the Fermi energy EF. When the Fermi level is located at the VBM, the value of EF is zero. Different chemical potential conditions have significant influence on the formation energies of defects, determining the defect concentrations in CrX3. Three typical positions in the stable chemical potential region of CrX3 are considered, as shown in Figure 3. At point A, the value of ΔμCr is the smallest, corresponding to a Cr-rich/X-poor condition. At point C, ΔμX is close to the elemental substance halogen, corresponding to a Cr-poor/X-rich condition. Point B is in the middle of the stable chemical potential region, thus corresponding to a moderate growth condition.

growth can be determined, as shown in Figure 3a−c. In experiments, Cr powder and elementary substance Cl2/Br2/I2 are used for synthesis. Based on the phase diagram in Figure 3, byproduct CrX2 may also be synthesized. Taking CrCl3 in Figure 3a as an example, CrCl2 will form when the (ΔμCr, ΔμCl) point is on the left-hand side of the A−D line. It is important therefore to control the stoichiometric proportion of Cr and X2 when synthesizing CrX3. From Figure 3, we obtain the stable areas for CrCl3, CrBr3, and CrI3 growth: 21.34, 19.33, and 9.96% of the entire area, respectively. In other words, the size of the stable chemical potential region becomes smaller with increasing the atomic number of X. It is known that the oxidation capacity of halogen decreases with increasing atomicity. Therefore, the growth of CrCl3 and CrBr3 is easier than that of CrI3. It has already been demonstrated that the growth of CrX3 can be achieved by using a chemical vapor transport method with an appropriate temperature gradient.31 3.4. Formation Energies of Point Defects. To simulate the formation of point defects in CrX3, the formation energies of a series of defects are calculated using supercell methods. 18860


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Figure 5. Spin-polarized partial DOS of (a) pristine CrI3, (b) VCr, (c) VI, and (d) iI. Top views of (e) VCr and (f) VI. (g) Top view and (h) side view of iI.

conduction band edges are fully spin-polarized, which is consistent with the band structure of CrI3 in Figure 2c. For CrI3 with VCr defects, there is only one empty state in the band gap, which is shown in Figure 5b. The spin-polarized DOS of CrI3 with VI in Figure 5c shows that there are two localized defect states in the middle of the band gap, which is consistent with a previous work.24 Both the states are in the middle band gap, indicating the deep level defect nature of VI. There are also two empty localized defect states in the middle of the band gap for iI, as shown in Figure 5d. The interstitial position of I for iI can be found in Figure 5g,h. From the top and side views, we find that iI is close to I atoms and the two defect states are therefore mainly attributed to I atoms, which is consistent with the partial DOS of I p orbitals in Figure 5d. By using Löwdin charge analysis, we obtain the magnetic moment of a unit cell for CrX3 to be 3.00 μB and the local magnetic moment of Cr/I to be 3.34/−0.12 μB, indicating that the origin of the ferromagnetism is from Cr atoms. The localized states induced by intrinsic defects will alter the spin density distribution. We studied the local magnetic moments of Cr and I atoms near the intrinsic defects. For a VI defect, the magnetic moment of nearby Cr/I changes to 3.72/−0.10 μB, which is close to that of pristine CrI3. However, for VCr, the change of magnetic moment of nearby Cr is reduced to 3.19 μB and that of nearby I is enhanced to −0.34. Because the interstitial I atom of iI is close to one I atom in CrI3, there is strong interaction between the two I atoms. The magnetic

Figure 4 shows the defect formation energies of various point defects of CrX3 as a function of the Fermi level under different chemical potential conditions (Cr-rich, moderate, and poor). From Figure 4, we can see that most point defects are energetically unfavorable to form under the three different conditions because of their positive formation energies, except VCr in CrCl3 under Cr-poor conditions (see Figure 4c). This indicates that most point defects are difficult to form with the exception of VCr in CrCl3, which can be formed under electron-rich conditions. Though intrinsic point defects are difficult to form in CrX3 during the synthesis process, the defects can be engineered afterward by various methods, such as pulsed laser deposition,32 chemical doping,33 and plasma treatment.34 In addition, it has been predicted that defect engineering will improve the magnetic properties of CrX3. For example, the Curie temperatures of CrX3 can be tuned by hole doping.35 Recently, it has been predicted that I-vacancy (VI) in CrI3 can enhance the intrinsic ferromagnetism and induce switchable electric polarization.24 According to the formation energies of various defects in Figure 4, the most promising defects are iX, VCr, and VX. Therefore, it is important to investigate the effect of intrinsic point defects (iX, VCr, and VX) on the electronic properties of CrX3. 3.5. Effect of Defects on Electronic and Magnetic Properties. Figure 5 shows the spin-polarized density of states (DOS) of pristine CrI3 and CrI3 with VCr, VI, and iI defects. From Figure 5a, we can see that the valence band and 18861


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Figure 6. (a) Scheme of the WSe2/CrI3 van der Waals heterostructure. The red dotted circles represent Cr-vacancy and I-vacancy, respectively. (b,c) Schemes of conduction and valence band edges around the +K/−K point for pristine WSe2 and WSe2/CrI3, respectively. Spin-resolved band structures from WSe2 contribution for (d) WSe2/CrI3, (e) WSe2/VCr-CrI3, and (f) WSe2/VI-CrI3.

moments of interstitial and nearby I atoms are −0.12 and 0.12 μB, while that of nearby Cr is reduced to 0.60 μB. Therefore, we claim that CrI3 with defects remains a robust ferromagnetic insulator, even though there is spin density redistribution. Here, we only discussed CrI3, but most conclusions are also valid for CrCl3 and CrBr3. 3.6. Valley Splitting of WSe2 on CrI3 with Defects. One application of CrI3 is to induce valley splitting in single-layer transition-metal dichalcogenides.18 WSe2 and single-layer CrI3 van der Waals heterojunctions (WSe2/CrI3) are shown in Figure 6a. Figure 6b shows the scheme of band edges around K valleys for pristine single-layer transition-metal dichalcogenide. Because of a magnetic field or magnetic exchange field induced by the proximity effect or magnetic doping, the energy of band edges around K valleys in WSe2 will split, as shown in Figure 6c. This is generally called “valley splitting”. The value of valley splitting Δ can be evaluated by considering the transition energy difference between the conduction band edge and the valence band edge with the same spin, as shown in Figure 6c. The value of Δ is 1.28 meV for WSe2/CrI3, found by analyzing the band structure, as shown in Figure 6d. The positions of VCr and VI are shown in Figure 6a. It has been reported that the electric field36 and stacking order37 will affect the value of valley splitting in WSe2/CrI3. Here, we focus on the effect of defects on the valley splitting. The valley splitting is reported to be 3.5 meV for WSe2 on multilayer CrI3 at 5 K.18 Our predicted splitting value is of the same order of magnitude. The difference between calculated and experimental values can be attributed to the following reasons. First, multilayer CrI3 is used in experiments, while single-layer CrI3 is used in our calculationlayer thickness may play a role in interlayer interaction. Second, mechanical exfoliation and dry transfer methods are employed to build a WSe2/CrI3 heterojunction18there may be some defects generated on the CrI3 surface. Third, stacking order38 and twist angle between layers39,40 are crucial factors affecting the electronic properties of a van der Waals heterojunctionthe stacking order and twist angle are not controlled and are therefore unknown in the experiment.18 There may also be inconsistencies between our WSe2/CrI3 model and experimental samples. Figure 6e,f shows that the valley splitting remains for WSe2 on CrI3 with VCr (VCr-CrI3) and VI (VI-CrI3), with the values of Δ increasing to 8.61 and 11.38 meV, respectively. This indicates that the existence of vacancies not only retains the ferromagnetic contribution from CrI3 but also enhances valley

splitting. The interlayer distance d of WSe2/CrI3 is defined as the distance between the Se and I plane, as shown in Figure 6a. The d reduces to 3.71 Å for WSe2/CrI3 and to 3.64 Å and 3.69 Å for WSe2/VCr-CrI3 and WSe2/VI-CrI3, respectively, indicating an increase in the layer−layer interaction. From the discussion of defect states shown in Figure 5, we conclude that vacancies lead to interlayer electron density and spin density redistribution. Therefore, the increase in valley splitting induced by vacancies can be attributed to an increased interaction and electron redistribution between WSe2 and CrI3. The vacancy density is an important factor in experiments. If the vacancy density is high, then the interaction of vacancies will occur, altering the electronic structure of the heterojunction. Also, the effect of vacancy disorder on magnetic properties has not been considered in our prediction. We only considered VCr and VI at the interface of WSe2/CrI3 in the present work. Because of iI increasing the d, the WSe2/CrI3 interaction would be reduced, which may not enhance valley splitting. Therefore, we have not studied iI in WSe2/CrI3 in our present work. It is expected that the significant enhancement of valley splitting induced by vacancies can stimulate experimental development.

4. CONCLUSIONS In conclusion, we have applied first-principles calculations to study the physics of intrinsic defects in CrX3. Comparing the chemical potential phase diagrams, we find that all three kinds of CrX3 are easy to grow. The concentration of most point defects in CrX3 are very low because of their high formation energies. Because of the large effective carrier mass and low carrier mobility, we claim that CrX3 is a family of insulators rather than semiconductors. From the defect physics study, we studied the effect of VI, VCr, and iI point defects on the electronic properties of CrI3 and conclude that CrI3 is a robust ferromagnetic insulator against defects. Moreover, VCr and VI at the interfaces between the WSe2/CrI3 van der Waals heterojunction can strongly improve the valley splitting in WSe2 due to the enhancement of interlayer interaction.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (Q.S.). *E-mail: [email protected] (Y.C.). ORCID

Qian Shen: 0000-0002-7197-2574 18862


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(15) Deng, Y.; Yu, Y.; Song, Y.; Zhang, J.; Wang, N. Z.; Sun, Z.; Yi, Y.; Wu, Y. Z.; Wu, S.; Zhu, J.; Wang, J.; Chen, X. H.; Zhang, Y. GateTunable Room-Temperature Ferromagnetism in Two-Dimensional Fe3GeTe2. Nature 2018, 563, 94−99. (16) Gong, C.; Li, L.; Li, Z.; Ji, H.; Stern, A.; Xia, Y.; Cao, T.; Bao, W.; Wang, C.; Wang, Y.; Qiu, Z. Q.; Cava, R. J.; Louie, S. G.; Xia, J.; Zhang, X. Discovery of Intrinsic Ferromagnetism in Two-Dimensional van der Waals Crystals. Nature 2017, 546, 265−269. (17) Ghazaryan, D.; Greenaway, M. T.; Wang, Z.; GuarochicoMoreira, V. H.; Vera-Marun, I. J.; Yin, J.; Liao, Y.; Morozov, S. V.; Kristanovski, O.; Lichtenstein, A. I.; Katsnelson, M. I.; Withers, F.; Mishchenko, A.; Eaves, L.; Geim, A. K.; Novoselov, K. S.; Misra, A. Magnon-Assisted Tunnelling in van der Waals Heterostructures Based on CrBr3. Nat. Electron. 2018, 1, 344−349. (18) Zhong, D.; Seyler, K. L.; Linpeng, X.; Cheng, R.; Sivadas, N.; Huang, B.; Schmidgall, E.; Taniguchi, T.; Watanabe, K.; McGuire, M. A.; Yao, W.; Xiao, D.; Fu, K. C.; Xu, X. Van der Waals Engineering of Ferromagnetic Semiconductor Heterostructures for Spin and Valleytronics. Sci. Adv. 2017, 3, No. e1603113. (19) Kou, L.; Hu, F.; Yan, B.; Wehling, T.; Felser, C.; Frauenheim, T.; Chen, C. Proximity Enhanced Quantum Spin Hall State in Graphene. Carbon 2015, 87, 418−423. (20) Feng, N.; Mi, W.; Cheng, Y.; Guo, Z.; Schwingenschlögl, U.; Bai, H. Magnetism by Interfacial Hybridization and p-type Doping of MoS2 in Fe4N/MoS2 Superlattices: A First-Principles Study. ACS Appl. Mater. Interfaces 2014, 6, 4587−4594. (21) Xue, X.; Wang, X.; Mi, W. Valley and Spin Splitting in Monolayer TX2/Antiferromagnetic MnO (T = Mo, W; X = S, Se) van der Waals Heterostructures. J. Phys. D: Appl. Phys. 2019, 52, 115303. (22) Song, Y.; Wang, X.; Mi, W. Ferroelectricity Tailored Valley Splitting in Monolayer WTe2/YMnO3 Heterostructures: A Route toward Electrically Controlled Valleytronics. Adv. Electron. Mater. 2017, 3, 1700245. (23) Lin, G. T.; Luo, X.; Chen, F. C.; Yan, J.; Gao, J. J.; Sun, Y.; Tong, W.; Tong, P.; Lu, W. J.; Sheng, Z. G.; Song, W. H.; Zhu, X. B.; Sun, Y. P. Critical Behavior of Two-Dimensional Intrinsically Ferromagnetic Semiconductor CrI3. Appl. Phys. Lett. 2018, 112, 072405. (24) Zhao, Y.; Lin, L.; Zhou, Q.; Li, Y.; Yuan, S.; Chen, Q.; Dong, S.; Wang, J. Surface Vacancy-Induced Switchable Electric Polarization and Enhanced Ferromagnetism in Monolayer Metal Trihalides. Nano Lett. 2018, 18, 2943−2949. (25) Giannozzi, P.; Baroni, S.; Bonini, N.; Calandra, M.; Car, R.; Cavazzoni, C.; Ceresoli, D.; Chiarotti, G. L.; Cococcioni, M.; Dabo, I.; Dal Corso, A.; de Gironcoli, S.; Fabris, S.; Fratesi, G.; Gebauer, R.; Gerstmann, U.; Gougoussis, C.; Kokalj, A.; Lazzeri, M.; MartinSamos, L.; Marzari, N.; Mauri, F.; Mazzarello, R.; Paolini, S.; Pasquarello, A.; Paulatto, L.; Sbraccia, C.; Scandolo, S.; Sclauzero, G.; Seitsonen, A. P.; Smogunov, A.; Umari, P.; Wentzcovitch, R. M. Quantum Espresso: A Modular and Open-Source Software Project for Quantum Simulations of Materials. J. Phys.: Condens. Matter 2009, 21, 395502. (26) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (27) Van de Walle, C. G.; Neugebauer, J. First-Principles Calculations for Defects and Impurities: Applications to Iii-Nitrides. J. Appl. Phys. 2004, 95, 3851−3879. (28) Cai, Y.; Zhang, G.; Zhang, Y.-W. Polarity-Reversed Robust Carrier Mobility in Monolayer MoS2 Nanoribbons. J. Am. Chem. Soc. 2014, 136, 6269−6275. (29) Yun, W. S.; Han, S. W.; Hong, S. C.; Kim, I. G.; Lee, J. D. Thickness and Strain Effects on Electronic Structures of Transition Metal Dichalcogenides: 2H-MX2 Semiconductors (M = Mo, W; X = S, Se, Te). Phys. Rev. B: Condens. Matter Mater. Phys. 2012, 85, 033305. (30) Ong, S. P.; Richards, W. D.; Jain, A.; Hautier, G.; Kocher, M.; Cholia, S.; Gunter, D.; Chevrier, V. L.; Persson, K. A.; Ceder, G. Python Materials Genomics (Pymatgen): A Robust, Open-Source

Yingchun Cheng: 0000-0002-8495-9184 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (nos. 61575094, 21673118 and 91833302). This work was also sponsored by Qing Lan Project and the Jiangsu Specially-Appointed Professor programme. We are grateful to the High Performance Computing Center of Nanjing Tech University for supporting the computational resources.

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REFERENCES

(1) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Zhang, Y.; Dubonos, S. V.; Grigorieva, I. V.; Firsov, A. A. Electric Field Effect in Atomically Thin Carbon Films. Science 2004, 306, 666−669. (2) Dean, C. R.; Young, A. F.; Meric, I.; Lee, C.; Wang, L.; Sorgenfrei, S.; Watanabe, K.; Taniguchi, T.; Kim, P.; Shepard, K. L.; Hone, J. Boron Nitride Substrates for High-Quality Graphene Electronics. Nat. Nanotechnol. 2010, 5, 722−726. (3) Wang, Q. H.; Kalantar-Zadeh, K.; Kis, A.; Coleman, J. N.; Strano, M. S. Electronics and Optoelectronics of Two-Dimensional Transition Metal Dichalcogenides. Nat. Nanotechnol. 2012, 7, 699− 712. (4) Naguib, M.; Come, J.; Dyatkin, B.; Presser, V.; Taberna, P.-L.; Simon, P.; Barsoum, M. W.; Gogotsi, Y. A Promising Transition Metal Carbide Anode for Lithium-Ion Batteries. Electrochem. Commun. 2012, 16, 61−64. (5) Xiao, D.; Liu, G. B.; Feng, W.; Xu, X.; Yao, W. Coupled Spin and Valley Physics in Monolayers of MoS2 and Other Group-VI Dichalcogenides. Phys. Rev. Lett. 2012, 108, 196802. (6) Zhu, Z. Y.; Cheng, Y. C.; Schwingenschlögl, U. Giant SpinOrbit-Induced Spin Splitting in Two-Dimensional Transition-Metal Dichalcogenide Semiconductors. Phys. Rev. B: Condens. Matter Mater. Phys. 2011, 84, 153402. (7) MacNeill, D.; Heikes, C.; Mak, K. F.; Anderson, Z.; Kormanyos, A.; Zolyomi, V.; Park, J.; Ralph, D. C. Breaking of Valley Degeneracy by Magnetic Field in Monolayer MoSe2. Phys. Rev. Lett. 2015, 114, 037401. (8) Song, X.; Xie, S.; Kang, K.; Park, J.; Sih, V. Long-Lived Hole Spin/Valley Polarization Probed by Kerr Rotation in Monolayer WSe2. Nano Lett. 2016, 16, 5010−5014. (9) Zhang, Q.; Yang, S. A.; Mi, W.; Cheng, Y.; Schwingenschlögl, U. Large Spin-Valley Polarization in Monolayer MoTe2 on Top of Euo(111). Adv. Mater. 2016, 28, 959−966. (10) Qi, J. S.; Li, X.; Niu, Q.; Feng, J. Giant and Tunable Valley Degeneracy Splitting in MoTe2. Physical Review B: Condensed Matter and Materials Physics 2015, 92, 121403. (11) Zhao, C.; Norden, T.; Zhang, P. Y.; Zhao, P. Q.; Cheng, Y. C.; Sun, F.; Parry, J. P.; Taheri, P.; Wang, J. Q.; Yang, Y. H.; Scrace, T.; Kang, K. F.; Yang, S.; Miao, G. X.; Sabirianov, R.; Kioseoglou, G.; Huang, W.; Petrou, A.; Zeng, H. Enhanced Valley Splitting in Monolayer WSe2 Due to Magnetic Exchange Field. Nat. Nanotechnol. 2017, 12, 757−762. (12) McGuire, M. A.; Dixit, H.; Cooper, V. R.; Sales, B. C. Coupling of Crystal Structure and Magnetism in the Layered, Ferromagnetic Insulator CrI3. Chem. Mater. 2015, 27, 612−620. (13) Zhang, W.-B.; Qu, Q.; Zhu, P.; Lam, C.-H. Robust Intrinsic Ferromagnetism and Half Semiconductivity in Stable Two-Dimensional Single-Layer Chromium Trihalides. J. Mater. Chem. C 2015, 3, 12457−12468. (14) Huang, B.; Clark, G.; Navarro-Moratalla, E.; Klein, D. R.; Cheng, R.; Seyler, K. L.; Zhong, D.; Schmidgall, E.; McGuire, M. A.; Cobden, D. H.; Yao, W.; Xiao, D.; Jarillo-Herrero, P.; Xu, X. LayerDependent Ferromagnetism in a van der Waals Crystal Down to the Monolayer Limit. Nature 2017, 546, 270−273. 18863


Research Article

ACS Applied Materials & Interfaces Python Library for Materials Analysis. Comput. Mater. Sci. 2013, 68, 314−319. (31) Abramchuk, M.; Jaszewski, S.; Metz, K. R.; Osterhoudt, G. B.; Wang, Y.; Burch, K. S.; Tafti, F. Controlling Magnetic and Optical Properties of the van der Waals Crystal CrCl3‑xBrx Via Mixed Halide Chemistry. Adv. Mater. 2018, 30, 1801325. (32) Wang, H.; Wang, Q.; Cheng, Y.; Li, K.; Yao, Y.; Zhang, Q.; Dong, C.; Wang, P.; Schwingenschlögl, U.; Yang, W.; Zhang, X. X. Doping Monolayer Graphene with Single Atom Substitutions. Nano Lett. 2012, 12, 141−144. (33) Zhou, D.; Pu, C.; He, C.; Zhang, F.; Lu, C.; Bao, G. PressureInduced Phase Transition of BiOF: Novel Two-Dimensional Layered Structures. Phys. Chem. Chem. Phys. 2015, 17, 4434−4440. (34) Shen, C.; Huang, G.; Cheng, Y.; Cao, R.; Ding, F.; Schwingenschlögl, U.; Mei, Y. Thinning and Functionalization of Few-Layer Graphene Sheets by CF4 Plasma Treatment. Nanoscale Res. Lett. 2012, 7, 268. (35) Liu, J.; Sun, Q.; Kawazoe, Y.; Jena, P. Exfoliating Biocompatible Ferromagnetic Cr-Trihalide Monolayers. Phys. Chem. Chem. Phys. 2016, 18, 8777−8784. (36) Xie, J.; Jia, L.; Shi, H.; Yang, D.; Si, M. Electric Field Mediated Large Valley Splitting in the van der Waals Heterostructure WSe2/ CrI3. Jpn. J. Appl. Phys. 2019, 58, 010906. (37) Zhang, Z.; Ni, X.; Huang, H.; Hu, L.; Liu, F. Valley Splitting in the van der Waals Heterostructure WSe2/CrI3: The Role of Atom Superposition. Phys. Rev. B 2019, 99, 115441. (38) Sivadas, N.; Okamoto, S.; Xu, X.; Fennie, C. J.; Xiao, D. Stacking-Dependent Magnetism in Bilayer CrI3. Nano Lett. 2018, 18, 7658−7664. (39) Cao, Y.; Fatemi, V.; Fang, S.; Watanabe, K.; Taniguchi, T.; Kaxiras, E.; Jarillo-Herrero, P. Unconventional Superconductivity in Magic-Angle Graphene Superlattices. Nature 2018, 556, 43−50. (40) Tong, Q.; Liu, F.; Xiao, J.; Yao, W. Skyrmions in the Moiré of van der Waals 2D Magnets. Nano Lett. 2018, 18, 7194−7199.

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Enhanced Valley Splitting of Transition-Metal Dichalcogenide by

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