Modelling of stacked 2D materials and devices

2D Materials

Volumn 2, Issue 3, 2015, Pages

  Qian, Xiaofeng ^a   Wang, Yangyang ^b,c   Li, Wenbin ^b   Lu, Jing ^c   Li, Ju ^b  

^a Department of Electrical and Computer Engineering   (United States)

^b Massachusetts Institute of Technology   (United States)

^c PEKING UNIVERSITY   (China)

Author keywords

Modeling and simulation; Stacked 2D material devices; Stacked 2D materials

Indexed keywords

BORON COMPOUNDS; LAYERED SEMICONDUCTORS; MOLYBDENUM COMPOUNDS;

MATERIAL CHOICE; MODEL AND SIMULATION; NEW DEVICES; PHYSICAL MECHANISM; STACKED 2D MATERIAL DEVICES; TWO-DIMENSIONAL MATERIALS;

SULFUR COMPOUNDS;

EID: 84953270126     PISSN: None     EISSN: 20531583     Source Type: Journal    
DOI: 10.1088/2053-1583/2/3/032003     Document Type: Review

References (166)

1. Novoselov KS, Geim AK, Morozov SV, Jiang D, Zhang Y, Dubonos SV, Grigorieva IV and Firsov A A 2004 Electric field effect in atomically thin carbon films Science 306 666-9
2. Geim AK 2011 Nobel Lecture: random walk to graphene Rev. Mod. Phys. 83 851-62
3. Novoselov KS 2011 Nobel lecture: graphene: materials in the flatland Rev. Mod. Phys. 83 837-49
4. Novoselov KS, Jiang D, Schedin F, Booth T J, Khotkevich VV, Morozov SV and Geim AK 2005 Two-dimensional atomic crystals PNAS 102 10451-3
5. Castro Neto AH, Guinea F, Peres NMR, Novoselov KS and Geim AK 2009 The electronic properties of graphene Rev. Mod. Phys. 81 109-62
6. Wang H, Yuan H, Sae Hong S, Li Y and Cui Y 2015 Physical and chemical tuning of two-dimensional transition metal dichalcogenides Chem. Soc. Rev. 44 2664-80
7. Wang QH, Kalantar-Zadeh K, Kis A, Coleman JN and Strano MS 2012 Electronics and optoelectronics of two-dimensional transition metal dichalcogenides Nature Nanotech. 7 699-712
8. Schwierz F 2010 Graphene transistors Nature Nanotech. 5 487-96
9. Britnell L et al 2012 Field-Effect Tunneling Transistor Based on Vertical Graphene Heterostructures Science 335 947-50
10. 2 Phototransistors with Spectral Response from Ultraviolet to Infrared Adv. Mater. 24 5832-6
11. 2 Nanosheet Phototransistors with Thickness-Modulated Optical Energy Gap Nano Lett. 12 3695-700
12. 2 phototransistors Acs Nano 6 74-80
13. Das S, Gulotty R, Sumant AV and Roelofs A 2014 All two-dimensional, flexible, transparent, and thinnest thin film transistor Nano Lett. 14 2861-6
14. Roy T, Tosun M, Kang J S, Sachid A B, Desai S B, Hettick M, Hu CC and Javey A 2014 Field-effect transistors built from all two-dimensional material components Acs Nano 8 6259-64
15. 2/WSe2 van der waals tunnel diodes and transistors Acs Nano 9 2071-9
16. Wang Y Y et al 2015 All-Metallic vertical transistors based on stacked dirac materials Adv. Funct. Mater. 25 68-77
17. Feng J, Qian X, Huang C-W and Li J 2012 Strain-engineered artificial atom as a broad-spectrum solar energy funnel Nature Photon. 6 866-72
18. Bernardi M, Palummo M and Grossman JC 2013 Extraordinary sunlight Absorption and One Nanometer Thick Photovoltaics Using Two-Dimensional Monolayer Materials Nano Lett. 13 3664-70
19. Pospischil A, Furchi MM and Mueller T 2014 Solar-energy conversion and light emission in an atomic monolayer p-n diode Nature Nanotech. 9 257-61
20. Shanmugam M, Jacobs-Gedrim R, Song E S and Yu B 2014 Two-dimensional layered semiconductor/graphene heterostructures for solar photovoltaic applications Nanoscale 6 12682-9
21. Furchi MM, Pospischil A, Libisch F, Burgdörfer J and Mueller T 2014 Photovoltaic effect in an electrically tunable van der waals heterojunction Nano Lett. 14 4785-91
22. Baugher BWH, Churchill HOH, Yang Y and Jarillo-Herrero P 2014 Optoelectronic devices based on electrically tunable p-n diodes in a monolayer dichalcogenide Nature Nanotech. 9 262-7
23. Ross J S et al 2014 Electrically tunable excitonic light-emitting diodes based on monolayer WSe2 p-n junctions Nature Nanotech. 9 268-72
24. 2 Nature Nanotech. 10 151-5
25. Salehzadeh O, Tran NH, Liu X, Shih I and Mi Z 2014 Exciton kinetics, quantum efficiency, and efficiency droop of monolayer mos2 light-emitting devices Nano Lett. 14 4125-30
26. Wu S et al 2014 Control of two-dimensional excitonic light emission via photonic crystal 2D Mater. 1 011001
27. Withers F et al 2015 Light-emitting diodes by band-structure engineering in van der Waals heterostructures Nature Mater. 14 301-6
28. Zhang Y J, Oka T, Suzuki R, Ye J T and Iwasa Y 2014 Electrically switchable chiral light-emitting transistor Science 344 725-8
29. 2 films Adv. Funct. Mater. 23 5511-7
30. 2 thin-film transistor arrays for practical gas-sensing applications Small 8 2994-9
31. 2 film-based field-effect transistors for sensing no at room temperature Small 8 63-7
32. 2 transistors Acs Nano 7 4879-91
33. 2 Nature Nanotech. 8 497-501
34. 2 Nano Lett. 13 668-73
35. 2 transistors Acs Nano 8 5304-14
36. 2 field-effect transistor for nextgeneration label-free biosensors Acs Nano 8 3992-4003
37. Schedin F, Geim AK, Morozov SV, Hill EW, Blake P, Katsnelson MI and Novoselov KS 2007 Detection of individual gas molecules adsorbed on graphene Nature Mater. 6 652-5
38. Wehling TO, Novoselov KS, Morozov SV, Vdovin E E, Katsnelson MI, Geim AK and Lichtenstein A I 2008 Molecular doping of graphene Nano Lett. 8 173-7
39. Liu J, Hsieh TH, Wei P, Duan W, Moodera J and Fu L 2014 Spin-filtered edge states with an electrically tunable gap in a two-dimensional topological crystalline insulator Nature Mater. 13 178-83
40. Qian X, Liu J, Fu L and Li J 2014 Quantum spin hall effect in two-dimensional transition metal dichalcogenides Science 346 1344-7
41. Geim AK and Grigorieva IV 2013 Van der waals heterostructures Nature 499 419-25
42. Decker R, Wang Y, Brar VW, Regan W, Tsai H-Z, Wu Q, Gannett W, Zettl A and Crommie MF 2011 Local Electronic Properties of Graphene on a BNSubstrate via Scanning Tunneling Microscopy Nano Lett. 11 2291-5
43. Dean CR et al 2010 Boron nitride substrates for high-quality graphene electronics Nature Nanotech. 5 722-6
44. Britnell L et al 2012 Electron tunneling through ultrathin boron nitride crystalline barriers Nano Lett. 12 1707-10
45. Mishchenko A et al 2014 Twist-controlled resonant tunnelling in graphene/boron nitride/graphene heterostructures Nature Nanotech. 9 808-13
46. Brey L 2014 Coherent tunneling and negative differential conductivity in a graphene/h-bn/graphene heterostructure Phys. Rev. Appl. 2 014003
47. Roth S, Matsui F, Greber T and Osterwalder J 2013 Chemical vapor deposition and characterization of aligned and incommensurate graphene/hexagonal boron nitride heterostack on Cu (111) Nano Lett. 13 2668-75
48. Yang W et al 2013 Epitaxial growth of single-domain graphene on hexagonal boron nitride Nature Mater. 12 792-7
49. Tang S et al 2013 Precisely aligned graphene grown on hexagonal boron nitride by catalyst free chemical vapor deposition Sci. Rep. 3 2666
50. Xue J, Sanchez-Yamagishi J, Bulmash D, Jacquod P, Deshpande A, Watanabe K, Taniguchi T, Jarillo-Herrero P and Le Roy B J 2011 Scanning tunnelling microscopy and spectroscopy of ultra-flat graphene on hexagonal boron nitride Nature Mater. 10 282-5
51. Dean CR et al 2013 Hofstadter's butterfly and the fractal quantum Hall effect in Moiré superlattices Nature 497 598-602
52. Yankowitz M, Xue J, Cormode D, Sanchez-Yamagishi JD, Watanabe K, Taniguchi T, Jarillo-Herrero P, Jacquod P and Le Roy B J 2012 Emergence of superlattice dirac points in graphene on hexagonal boron nitride Nature Phys. 8 382-6
53. Sławiñska J, Zasada I and Klusek Z 2010 Energy gap tuning in graphene on hexagonal boron nitride bilayer system Phys. Rev. B 81 155433
54. Balu R, Zhong X, Pandey R and Karna S P 2012 Effect of electric field on the band structure of graphene/boron nitride and boron nitride/boron nitride bilayers Appl. Phys. Lett. 100 052104
55. Zhong X, Yap YK, Pandey R and Karna S P 2011 Firstprinciples study of strain-induced modulation of energy gaps of graphene/BN and BNbilayers Phys. Rev. B 83 193403
56. Giovannetti G, Khomyakov P A, Brocks G, Kelly P J and Van Den Brink J 2007 Substrate-induced band gap in graphene on hexagonal boron nitride: Ab initio density functional calculations Phys. Rev. B 76 073103
57. Quhe R et al 2012 Tunable and sizable band gap of singlelayer graphene sandwiched between hexagonal boron nitride NPG Asia Mater. 4 e6
58. Zhong X, Amorim RG, Scheicher RH, Pandey R and Karna S P 2012 Electronic structure and quantum transport properties of trilayers formed from graphene and boron nitride Nanoscale 4 5490-8
59. Ramasubramaniam A, Naveh D and Towe E 2011 Tunable band gaps in bilayer graphene-BNheterostructures Nano Lett. 11 1070-5
60. Bokdam M, Khomyakov P A, Brocks G, Zhong Z and Kelly P J 2011 Electrostatic doping of graphene through ultrathin hexagonal boron nitride films Nano Lett. 11 4631-5
61. Woods CR et al 2014 Commensurate-incommensurate transition in graphene on hexagonal boron nitride Nature Phys. 10 451-6
62. Ponomarenko L A et al 2013 Cloning of Dirac fermions in graphene superlattices Nature 497 594-7
63. Hunt B et al 2013 Massive dirac fermions and hofstadter butterfly in a van der waals heterostructure Science 340 1427-30
64. Yu GL et al 2014 Hierarchy of Hofstadter states and replica quantum Hall ferromagnetism in graphene superlattices Nature Phys. 10 525-9
65. Sachs B, Wehling TO, Katsnelson MI and Lichtenstein AI 2011 Adhesion and electronic structure of graphene on hexagonal boron nitride substrates Phys. Rev. B 84 195414
66. Ortix C, Yang L and Van Den Brink J 2012 Graphene on incommensurate substrates: Trigonal warping and emerging Dirac cone replicas with halved group velocity Phys. Rev. B 86 081405
67. Kindermann M, Uchoa B and Miller DL 2012 Zero-energy modes and gate-tunable gap in graphene on hexagonal boron nitride Phys. Rev. B 86 115415
68. Wallbank J R, Patel A A, Mucha-Kruczyñski M, Geim AK and Fal'ko VI 2013 Generic miniband structure of graphene on a hexagonal substrate Phys. Rev. B 87 245408
69. Mucha-Kruczyñski M, Wallbank J R and Fal'ko VI 2013 Heterostructures of bilayer graphene and h-BN: Interplay between misalignment, interlayer asymmetry, and trigonal warping Phys. Rev. B 88 205418
70. Jung J, Raoux A, Qiao Z and MacDonald AH 2014 Ab initio theory of moiré superlattice bands in layered two-dimensional materials Phys. Rev. B 89 205414
71. San-Jose P, Gutiérrez-Rubio A, Sturla M and Guinea F 2014 Spontaneous strains and gap in graphene on boron nitride Phys. Rev. B 90 075428
72. Bokdam M, Amlaki T, Brocks G and Kelly P J 2014 Band gaps in incommensurable graphene on hexagonal boron nitride Phys. Rev. B 89 201404
73. Neek-Amal M and Peeters FM 2014 Graphene on boronnitride: Moiré pattern in the van der Waals energy Appl. Phys. Lett. 104 041909
74. Moon P and Koshino M 2014 Electronic properties of graphene/hexagonal-boron-nitride Moiré superlattice Phys. Rev. B 90 155406
75. Nair R R, Blake P, Grigorenko AN, Novoselov KS, Booth T J, Stauber T, Peres NMR and Geim AK 2008 Fine Structure Constant Defines Visual Transparency of Graphene Science 320 1308
76. 2 hybrid structures for multifunctional photoresponsive memory devices Nature Nanotech. 8 826-30
77. 2 heterostructures Sci. Rep. 4 3826
78. Britnell L et al 2013 Strong light-matter Interactions in heterostructures of atomically thin films Science 340 1311-4
79. Yu WJ, Liu Y, Zhou H, Yin A, Li Z, Huang Y and Duan X 2013 Highly efficient gate-tunable photocurrent generation in vertical heterostructures of layered materials Nature Nanotech. 8 952-8
80. 2 heterojunction p-n Diodes Nano Lett. 14 5590-7
81. 2 heterostructures Nano Lett. 15 486-91
82. Gregg B A 2005 The Photoconversion Mechanism of Excitonic Solar Cells MRSBull. 30 20-2
83. Brumfiel G 2013 Sticky problem snares wonder material Nature 495 152-3
84. Liu H, Neal A T, Zhu Z, Luo Z, Xu X, Tománek D and Ye PD 2014 Phosphorene: An Unexplored 2D Semiconductor with a High Hole Mobility ACS Nano 8 4033-41
85. Brent J R, Savjani N, Lewis E A, Haigh S J, Lewis DJ and O'Brien P 2014 Production of few-layer phosphorene by liquid exfoliation of black phosphorus Chem. Commun. 50 13338-41
86. Lu W, Nan H, Hong J, Chen Y, Zhu C, Liang Z, Ma X, Ni Z, Jin C and Zhang Z 2014 Plasma-assisted fabrication of monolayer phosphorene and its Raman characterization Nano Research 7 853-9
87. Das S, Zhang W, Demarteau M, Hoffmann A, Dubey M and Roelofs A 2014 Tunable Transport Gap in Phosphorene Nano Lett. 14 5733-9
88. Das S, Demarteau M and Roelofs A 2014 Ambipolar phosphorene field effect transistor ACS Nano 8 11730-8
89. Li L, Yu Y, Ye GJ, Ge Q, Ou X, Wu H, Feng D, Chen XH and Zhang Y 2014 Black phosphorus field-effect transistors Nature Nanotech. 9 372-7
90. Du Y, Liu H, Deng Y and Ye PD 2014 Device perspective for black phosphorus field-effect transistors: contact resistance, ambipolar behavior, and scaling ACS Nano 8 10035-42
91. Han L, Neal A T, Mengwei S, Yuchen D and Ye PD 2014 The effect of dielectric capping on few-layer phosphorene transistors: tuning the schottky barrier heights Electron Device Letters, IEEE 35 795-7
92. Wood JD, Wells SA, Jariwala D, Chen K-S, Cho E, Sangwan VK, Liu X, Lauhon L J, Marks T J and Hersam MC 2014 Effective passivation of exfoliated black phosphorus transistors against ambient degradation Nano Lett. 14 6964-70
93. Na J, Lee Y T, Lim J A, Hwang DK, Kim G-T, Choi WK and Song Y-W 2014 Few-layer black phosphorus field-effect transistors with reduced current fluctuation ACS Nano 8 11753-62
94. Engel M, Steiner M and Avouris P 2014 Black phosphorus photodetector for multispectral, high-resolution imaging Nano Lett. 14 6414-7
95. Dai J and Zeng X C 2014 bilayer phosphorene: effect of stacking order on bandgap and its potential applications in thin-film solar cells J. Phys. Chem. Lett. 5 1289-93
96. 2 van der waals heterojunction p. n diode ACS Nano 8 8292-9
97. Padilha J E, Fazzio A and Da Silva A J R 2015 van der waals heterostructure of phosphorene and graphene: tuning the schottky barrier and doping by electrostatic gating Phys. Rev. Lett. 114 066803
98. Li J, Shan Z and Ma E 2014 Elastic strain engineering for unprecedented materials properties MRS Bull. 39 108-14
99. Havener RW, Zhuang H, Brown L, Hennig RG and Park J 2012 Angle-resolved raman imaging of interlayer rotations and interactions in twisted bilayer graphene Nano Lett. 12 3162-7
100. Kim K, Coh S, Tan L Z, Regan W, Yuk JM, Chatterjee E, Crommie MF, Cohen ML, Louie SG and Zettl A 2012 Raman spectroscopy study of rotated double-layer graphene: misorientation-angle dependence of electronic structure Phys. Rev. Lett. 108 246103
101. Li G, Luican A, Lopes Dos Santos JMB, Castro Neto AH, Reina A, Kong J and Andrei E Y 2010 Observation of Van hove singularities in twisted graphene layers Nature Phys. 6 109-13
102. Trambly De Laissardiere G, Mayou D and Magaud L 2010 Localization of dirac electrons in rotated graphene bilayers Nano Lett. 10 804-8
103. Luican A, Li G, Reina A, Kong J, Nair R R, Novoselov KS, Geim AK and Andrei E Y 2011 Single-layer behavior and its breakdown in twisted graphene layers Phys. Rev. Lett. 106 126802
104. Bistritzer R and MacDonald AH 2011 Moire bands in twisted double-layer graphene PNAS 108 12233-7
105. Novoselov KS, McCann E, Morozov SV, Fal'ko VI, Katsnelson MI, Zeitler U, Jiang D, Schedin F and Geim AK 2006 Unconventional quantum hall effect and berry's phase of 2α in bilayer graphene Nature Phys. 2 177-80
106. Liu K, Zhang L, Cao T, Jin C, Qiu D, Zhou Q, Zettl A, Yang P, Louie SG and Wang F 2014 Evolution of interlayer coupling in twisted molybdenum disulfide bilayers Nature Commun. 5 4966
107. Wu M, Qian X and Li J 2014 Tunable exciton funnel using moire superlattice in twisted van der waals bilayer Nano Lett. 14 5350-7
108. Kushima A, Qian X, Zhao P, Zhang S and Li J 2015 Ripplocations in van der waals layers Nano Lett. 15 1302-8
109. Qi J S, Huang J Y, Feng J, Shi DN and Li J 2011 The possibility of chemically inert, graphene-based all-carbon electronic devices with 0.8 eV Gap ACS Nano 5 3475-82
110. Feng J, Li W, Qian X, Qi J, Qi L and Li J 2012 Patterning of graphene Nanoscale 4 4883-99
111. Sancho MP L, Sancho JML and Rubio J 1984 Quick iterative scheme for the calculation of transfer matrices: application to Mo (100) J. Phys. F: Met. Phys. 14 1205-15
112. Sancho MPL, Sancho JML and Rubio J 1985 Highly convergent schemes for calculation of bulk and surface green-functions J. Phys. F: Met. Phys. 15 851-8
113. Brandbyge M, Mozos J-L, Ordejon P, Taylor J and Stokbro K 2002 Density-functional method for nonequilibrium electron transport Phys. Rev. B 65 165401
114. Qian X, Li J and Yip S 2010 Calculating phase-coherent quantum transport in nanoelectronics with ab initio quasiatomic orbital basis set Phys. Rev. B 82 195442
115. Chhowalla M, Shin HS, Eda G, Li L J, Loh KP and Zhang H 2013 The chemistry of two-dimensional layered transition metal dichalcogenide nanosheets Nature Chem. 5 263-75
116. Bjorkman T, Gulans A, Krasheninnikov AV and Nieminen RM 2012 van der waals bonding in layered compounds from advanced density-functional firstprinciples Calculations Phys. Rev. Lett. 108 235502
117. Bjorkman T, Gulans A, Krasheninnikov AV and Nieminen RM 2012 Are we van der waals ready? J. Phys.: Condens. Matter 24 424218
118. 2 Nano Lett. 10 1271-5
119. 2: A New Direct-Gap Semiconductor Phys. Rev. Lett. 105 136805
120. 2 nanoparticles J. Phys. Chem. C111 16192-6
121. 2 using angleresolved photoemission spectroscopy Phys. Rev. Lett. 111 106801
122. 2: many-body effects and diversity of exciton states Phys. Rev. Lett. 111 216805
123. 2 from first principles Phys. Rev. B 86 241201 (R)
124. Ramasubramaniam A 2012 Large excitonic effects in monolayers of molybdenum and tungsten dichalcogenides Phys. Rev. B 86 115409
125. 2 Phys. Rev. B 85 205302
126. 2 Phys. Rev. B 83 245213
127. Yun WS, Han SW, Hong S C, Kim IG and Lee JD 2012 Thickness and strain effects on electronic structures of transition metal dichalcogenides:2H-MX2 semiconductors (M = Mo, W;X= S, Se, Te) Phys. Rev. B 85 033305
128. 2 Nano Lett. 12 5576-80
129. 2 Nature Nanotech. 9 111-5
130. 2 Acs Nano 7 791-7
131. Ye Z L, Cao T, O'Brien K, Zhu HY, Yin XB, Wang Y, Louie SG and Zhang X 2014 Probing excitonic dark states in single-layer tungsten disulphide Nature 513 214-8
132. 2 monolayers Nano Lett. 13 3447-54
133. 2 monolayers by optical pumping Nature Nanotech. 7 490-3
134. 2 by optical helicity Nature Nanotech. 7 494-8
135. Cao T et al 2012 Valley-selective circular dichroism of monolayer molybdenum disulphide Nature Commun. 3 887
136. Yao W, Xiao D and Niu Q 2008 Valley-dependent optoelectronics from inversion symmetry breaking Phys. Rev. B 77 235406
137. 2 and other group-VI dichalcogenidesPhys. Rev. Lett. 108 196802
138. Zhu Z Y, Cheng YC and Schwingenschlogl U 2011 Giant spin-orbit-induced spin splitting in two-dimensional transition-metal dichalcogenide semiconductors Phys. Rev. B 84 153402
139. Xu XD, Yao W, Xiao D and Heinz T F 2014 Spin and pseudospins in layered transition metal dichalcogenides Nature Phys. 10 343-50
140. Duerloo KA N, Ong MT and Reed E J 2012 Intrinsic Piezoelectricity in Two-Dimensional Materials J. Phys. Chem. Lett. 3 2871-6
141. 2 for energy conversion and piezotronics Nature 514 470-4
142. Michel KH and Verberck B 2009 Theory of elastic and piezoelectric effects in two-dimensional hexagonal boron nitride Phys. Rev. B 80 224301
143. Li W and Li J 2015 Piezoelectricity in two-dimensional group III monochalcogenides arXiv:1503.07379
144. Kane CL and Mele E J 2005 Quantum spin hall effect in graphene Phys. Rev. Lett. 95 226801
145. Kane CL and Mele E J 2005 Z2 topological order and the quantum spin hall effect Phys. Rev. Lett. 95 146802
146. Bernevig B A, Hughes T L and Zhang S-C 2006 Quantum spin hall effect and topological phase transition in hgte quantum wells Science 314 1757-61
147. Bernevig B A and Zhang S-C 2006 Quantum spin hall effect Phys. Rev. Lett. 96 106802
148. König M, Wiedmann S, Brüne C, Roth A, Buhmann H, Molenkamp LW, Qi X-L and Zhang S-C 2007 Quantum spin hall insulator state in hgte quantumwells Science 318 766-70
149. Hasan MZ and Kane CL 2010 Topological insulators Rev. Mod. Phys. 82 3045-67
150. Qi X-L and Zhang S-C 2011 Topological insulators and superconductors Rev. Mod. Phys. 83 1057-110
151. Du L, Knez I, Sullivan G and Du R-R 2015 Robust helical edge transport in gated InAs/GaSb bilayers Phys. Rev. Lett. 114 096802
152. Liu C-C, Feng W and Yao Y 2011 Quantum spin hall effect in silicene and two-dimensional germanium Phys. Rev. Lett. 107 076802
153. Xu Y, Yan B, Zhang H-J, Wang J, Xu G, Tang P, Duan W and Zhang S-C 2013 Large-gap quantum spin hall insulators in tin films Phys. Rev. Lett. 111 136804
154. 5: a paradigm for large-gap quantum spin hall insulators Phys. Rev. X4 011002
155. Liu C, Hughes T L, Qi X-L, Wang K and Zhang S-C 2008 Quantum spin hall effect in inverted type-II semiconductors Phys. Rev. Lett. 100 236601
156. Xiao D, Zhu W, Ran Y, Nagaosa N and Okamoto S 2011 Interface engineering of quantum Hall effects in digital transition metal oxide heterostructures Nature Commun. 2 596-596
157. Cazalilla MA, Ochoa H and Guinea F 2014 Quantum spin hall effect in two-dimensional crystals of transition-metal dichalcogenides Phys. Rev. Lett. 113 077201
158. Wilson JA and Yoffe AD 1969 The transition metal dichalcogenides discussion and interpretation of the observed optical, electrical and structural properties Adv. Phys. 18 193-335
159. 2 Acs Nano 6 7311
160. Hohenberg P and Kohn W 1964 Inhomogeneous electron gas Phys. Rev. B 136 B864
161. Kohn W and Sham L 1965 Self-consistent equations including exchange and correlation effects Phys. Rev. 140 1133
162. Hedin L 1965 New method for calculating the one-particle green's function with application to the electron-gas problem Phys. Rev. 139 A796-823
163. Hybertsen MS and Louie SG 1986 Electron correlation in semiconductors and insulators: Band gaps and quasiparticle energies Phys. Rev. B 34 5390-413
164. Fu L and Kane CL 2007 Topological insulators with inversion symmetry Phys. Rev. B 76 045302
165. Qian X, Li J, Qi L, Wang C-Z, Chan T-L, Yao Y-X, Ho K-M and Yip S 2008 Quasiatomic orbitals for ab initio tight-binding analysis Phys. Rev. B 78 245112
166. Marzari N, Mostofi A A, Yates J R, Souza I and Vanderbilt D 2012 Maximally localized Wannier functions: Theory and applications Rev. Mod. Phys. 84 1419-75