Quantum spin hall effect in two-dimensional crystals of transition-metal dichalcogenides

Physical Review Letters

Volumn 113, Issue 7, 2014, Pages

  Cazalilla, M A ^a,b   Ochoa, H ^c   Guinea, F ^c  

^a NATIONAL CENTER FOR THEORETICAL SCIENCES   (Taiwan)

^b DONOSTIA INTERNATIONAL PHYSICS CENTER DIPC   (Spain)

^c INSTITUTO DE CIENCIA DE MATERIALES DE MADRID   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

TOPOLOGY; TRANSITION METALS;

DICHALCOGENIDES; EDGE TRANSPORT; MULTI TERMINALS; QUANTUM SPIN HALL EFFECT; SPIN-POLARIZED; TOPOLOGICAL INSULATORS; TOPOLOGICAL PHASIS; TWO-DIMENSIONAL CRYSTALS;

CRYSTALS;

EID: 84908485722     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.113.077201     Document Type: Article

References (70)

1. Q.H. Wang, K. Kalantar-Zadeh, A. Kiss, J.N. Coleman, and M.S. Strano, Nat. Nanotechnol. 7, 699 (2012) and references therein. NNAABX 1748-3387 10.1038/nnano.2012.193
2. B. Radisavljevic, A. Radenovic, J. Brivio, V. Giacometti, and A. Kis, Nat. Nanotechnol. 6, 147 (2011); NNAABX 1748-3387 10.1038/nnano.2010.279
3. H. Nam, S. Wi, H. Rokni, M. Chen, G. Priessnitz, W. Lu, and X. Liang, ACS Nano 7, 5870 (2013). ANCAC3 1936-0851 10.1021/nn401093u
4. M.Z. Hassan and C.L. Kane, Rev. Mod. Phys. 82, 3045 (2010); RMPHAT 0034-6861 10.1103/RevModPhys.82.3045
5. X.-L. Qi and S.-C. Zhang, Rev. Mod. Phys. 83, 1057 (2011); RMPHAT 0034-6861 10.1103/RevModPhys.83.1057
6. B.A. Bernevig and T.L. Hughes, Topological Insulators and Topological Superconductors (Princeton University Press, Princeton, NJ, 2013), and references therein.
7. See, e.g., S.-C. Zhang, http://www.aip.org/industry/presentations/2011/ day2-8-Zhang/index.htm
8. M. König, S. Wiedmann, C. Brüne, A. Roth, H. Buhmann, L.W. Molenkamp, X.-L. Qi, and S.C. Zhang, Science 318, 766 (2007). SCIEAS 0036-8075 10.1126/science.1148047 (Pubitemid 351411764)
9. I. Knez, R.-R. Du, G. Sullivan, Phys. Rev. Lett. 107, 136603 (2011). PRLTAO 0031-9007 10.1103/PhysRevLett.107.136603
10. C. Weeks, J. Hu, J. Alicea, M. Franz, and R. Wu, Phys. Rev. X 1, 021001 (2011). PRXHAE 2160-3308 10.1103/PhysRevX.1.021001
11. C.L. Kane and E.J. Mele, Phys. Rev. Lett. 95, 226801 (2005). PRLTAO 0031-9007 10.1103/PhysRevLett.95.226801 (Pubitemid 41776999)
12. F. Guinea, M.I. Katsnelson, and A.K. Geim, Nat. Phys. 6, 30 (2010). NPAHAX 1745-2473 10.1038/nphys1420
13. N. Levy, S.A. Burke, K.L. Meaker, M. Panlasigui, A. Zettl, F. Guinea, A.H. Castro Neto, and M.F. Crommie, Science 329, 544 (2010); SCIEAS 0036-8075 10.1126/science.1191700
14. J. Lu, A.H. Castro Neto, and K.P. Loh, Nat. Commun. 3, 823 (2011). NCAOBW 2041-1723 10.1038/ncomms1818
15. M.A. Vozmediano, M.I. Katsnelson, and F. Guinea, Phys. Rep. 496, 109 (2010). PRPLCM 0370-1573 10.1016/j.physrep.2010.07.003
16. B.A. Bernevig and S.-C. Zhang, Phys. Rev. Lett. 96, 106802 (2006). PRLTAO 0031-9007 10.1103/PhysRevLett.96.106802
17. D. Xiao, G.-B. Liu, W. Feng, X. Xu, and W. Yao, Phys. Rev. Lett. 108, 196802 (2012). PRLTAO 0031-9007 10.1103/PhysRevLett.108.196802
18. E. Cappelluti, R. Roldán, J.A. Silva-Guillen, P. Ordejón, and F. Guinea, Phys. Rev. B 88, 075409 (2013). PRBMDO 1098-0121 10.1103/PhysRevB.88.075409
19. H. Ochoa and R. Roldán, Phys. Rev. B 87, 245421 (2013). PRBMDO 1098-0121 10.1103/PhysRevB.87.245421
20. Z.Y. Zhu, Y.C. Cheng, and U. Schwingenschlögl, Phys. Rev. B 84, 153402 (2011); PRBMDO 1098-0121 10.1103/PhysRevB.84.153402
21. W. Feng, Y. Yao, W. Zhu, J. Zhou, W. Yao, and D. Xiao, Phys. Rev. B 86, 165108 (2012); PRBMDO 1098-0121 10.1103/PhysRevB.86.165108
22. A. Kormányos, V. Zólyomi, N.D. Drummond, P. Rakyta, G. Burkard, and V.I. Fal'ko, Phys. Rev. B 88, 045416 (2013). PRBMDO 1098-0121 10.1103/PhysRevB.88.045416
23. W. Jin, Phys. Rev. Lett. 111, 106801 (2013); PRLTAO 0031-9007 10.1103/PhysRevLett.111.106801
24. S.K. Mahatha, K.D. Patel, and K.S.R. Menon, J. Phys. Condens. Matter 24, 475504 (2012). JCOMEL 0953-8984 10.1088/0953-8984/24/47/475504
25. K.F. Mak, C. Lee, J. Hone, J. Shan, and T.F. Heinz, Phys. Rev. Lett. 105, 136805 (2010); PRLTAO 0031-9007 10.1103/PhysRevLett.105.136805
26. W.S. Yun, S.W. Han, S.C. Hong, I.G. Kim, and J.D. Lee, Phys. Rev. B 85, 033305 (2012). PRBMDO 1098-0121 10.1103/PhysRevB.85.033305
27. L.D. Landau and E.M. Lifschitz, Theory of Elasticity (Pergamon Press, Oxford, 1959);
28. G.L. Bir and G.E. Pikus, Symmetry and Strain-Induced Effects in Semiconductors (Wiley, New York, 1974).
29. See Supplemental Material at http://link.aps.org/supplemental/10.1103/ PhysRevLett.113.077201, which also includes Refs. [8,9,14,22-31].
30. F.D.M. Haldane, Phys. Rev. Lett. 61, 2015 (1988). PRLTAO 0031-9007 10.1103/PhysRevLett.61.2015
31. The situation is very similar to what happens in realistic HgTe quantum wells, see, for instance, the discussion in J.I. Väyrynen, M. Goldstein, and L.I. Glazman, Phys. Rev. Lett. 110, 216402 (2013). PRLTAO 0031-9007 10.1103/PhysRevLett.110.216402
32. J.C. Slater and G.F. Koster, Phys. Rev. 94, 1498 (1954). PHRVAO 0031-899X 10.1103/PhysRev.94.1498
33. J.R. Wallbank, A.A. Patel, M. Mucha-Kruczyn'ski, A.K. Geim, and V.I. Fal'ko, Phys. Rev. B 87, 245408 (2013). PRBMDO 1098-0121 10.1103/PhysRevB.87. 245408
34. C.L. Kane and E.J. Mele, Phys. Rev. Lett. 95, 146802 (2005). PRLTAO 0031-9007 10.1103/PhysRevLett.95.146802 (Pubitemid 41777602)
35. S. Helveg, J.V. Lauritsen, E. Lægsgaard, I. Stensgaard, J.K. Nørskov, B.S. Clausen, H. Topsøe, and F. Besenbacher, Phys. Rev. Lett. 84, 951 (2000); PRLTAO 0031-9007 10.1103/PhysRevLett.84.951
36. M.V. Bollinger, J.V. Lauritsen, K.W. Jacobsen, J.K. Nørskov, S. Helveg, and F. Besenbacher, Phys. Rev. Lett. 87, 196803 (2001); PRLTAO 0031-9007 10.1103/PhysRevLett.87.196803
37. J.V. Lauritsen, M. Nyberg, R.T. Vang, M.V. Bollinger, B.S. Clausen, H. Topsøe, K.W. Jacobsen, E.Lægsgaard, J.K.Nørskov, and F. Besenbacher, Nanotechnology 14, 385 (2003); NNOTER 0957-4484 10.1088/0957-4484/14/3/306
38. J. Zhang, J.M. Soon, K.P. Loh, J. Yin, J. Ding, M.B. Sullivian, and P. Wu, Nano Lett. 7, 2370 (2007); NALEFD 1530-6984 10.1021/nl071016r (Pubitemid 47315554)
39. A. Vojvodic, B. Hinnemann, and J.K. Norskov, Phys. Rev. B 80, 125416 (2009); PRBMDO 1098-0121 10.1103/PhysRevB.80.125416
40. R.-L. Chu, G.-B. Liu, W. Yao, X. Xu, D. Xiao, and C. Zhang, Phys. Rev. B 89, 155317 (2014); PRBMDO 1098-0121 10.1103/PhysRevB.89.155317
41. G. Xu, arXiv:1308.5664.
42. K.F. Mak, K. He, J. Shan, and T.F. Heinz, Nat. Nanotechnol. 7, 494 (2012); NNAABX 1748-3387 10.1038/nnano.2012.96
43. B. Zhu, H. Zeng, J. Dai, Z. Gong, and X. Cui, arXiv:1403.6224.
44. P. Johari and V.B. Shenoy, ACS Nano 6, 5449 (2012); ANCAC3 1936-0851 10.1021/nn301320r
45. K. He, C. Poole, K.F. Mak, and J. Shan, Nano Lett. 13, 2931 (2013); NALEFD 1530-6984 10.1021/nl4013166
46. Q. Zhang, Y. Cheng, L.-Y. Gan, and U. Schwingenschlögl, Phys. Rev. B 88, 245447 (2013); PRBMDO 1098-0121 10.1103/PhysRevB.88.245447
47. H.J. Conley, B. Wang, J.I. Ziegler, R.F. Haglund, Jr., S.T. Pantelides, and K.I. Bolotin, Nano Lett. 13, 3626 (2013); NALEFD 1530-6984 10.1021/nl4014748
48. A. Castellanos-Gomez, R. Roldán, E. Cappelluti, M. Buscema, F. Guinea, H.S.J. van der Zant, and G.A. Steele, Nano Lett. 13, 5361 (2013). NALEFD 1530-6984 10.1021/nl402875m
49. M. König, H. Buhmann, L.W. Molenkamp, T. Hughes, C.-X. Liu, X.-L. Qi, and S.-C. Zhang, J. Phys. Soc. Jpn. 77, 031007 (2008); JUPSAU 0031-9015 10.1143/JPSJ.77.031007
50. A. Roth, C. Brune, H. Buhmann, L.W. Molenkamp, J. Maciejko, X.-L. Qi, and S.-C. Zhang, Science 325, 294 (2009); SCIEAS 0036-8075 10.1126/science.1174736
51. G.M. Gusev, Z.D. Kvon, O.A. Shegai, N.N. Mikhailov, S.A. Dvoretsky, and J.C. Portal, Phys. Rev. B 84, 121302(R) (2011); PRBMDO 1098-0121 10.1103/PhysRevB.84.121302
52. M. König, Phys. Rev. X 3, 021003 (2013); PRXHAE 2160-3308 10.1103/PhysRevX.3.021003
53. K.C. Nowack, arXiv:1212.2203.
54. M.A. Cazalilla, H. Ochoa, and F. Guinea (to be published).
55. R.C. Cooper, C. Lee, C.A. Marianetti, X. Wei, J. Hone, and J.W. Kysar, Phys. Rev. B 87, 035423 (2013). The value of (Equation presented) is obtained from the calculated Young's modulus (Equation presented) and Poisson's ratio (Equation presented) as (Equation presented). PRBMDO 1098-0121 10.1103/PhysRevB.87.035423
56. Y. Aharonov and A. Casher, Phys. Rev. A 19, 2461 (1979); PLRAAN 0556-2791 10.1103/PhysRevA.19.2461
57. M. Bander, Phys. Rev. B 41, 9028 (1990). PRBMDO 0163-1829 10.1103/PhysRevB.41.9028
58. (Equation presented) is assumed to be positive as in the uniform case. Note that (Equation presented) as (Equation presented), and therefore (Equation presented).
59. M. Taillefumier, V.K. Dugaev, B. Canals, C. Lacroix, and P. Bruno, Phys. Rev. B 78, 155330 (2008). PRBMDO 1098-0121 10.1103/PhysRevB.78.155330
60. T. Low, F. Guinea, and M.I. Katsnelson, Phys. Rev. B 83, 195436 (2011). PRBMDO 1098-0121 10.1103/PhysRevB.83.195436
61. I. Snyman, Phys. Rev. B 80, 054303 (2009). PRBMDO 1098-0121 10.1103/PhysRevB.80.054303
62. M. Yankowitz, J. Xue, D. Cormode, J.D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, P. Jarillo-Herrero, P. Jacquod, and B.J. LeRoy, Nat. Phys. 8, 382 (2012). NPAHAX 1745-2473 10.1038/nphys2272
63. L.A. Ponomarenko, Nature (London) 497, 594 (2013). NATUAS 0028-0836 10.1038/nature12187
64. C.R. Dean, Nature (London) 497, 598 (2013). NATUAS 0028-0836 10.1038/nature12186
65. B. Hunt, Science 340, 1427 (2013). SCIEAS 0036-8075 10.1126/science. 1237240
66. O.P. Sushkov and A.H. Castro Neto, Phys. Rev. Lett. 110, 186601 (2013). PRLTAO 0031-9007 10.1103/PhysRevLett.110.186601
67. C. Xu and J.E. Moore, Phys. Rev. B 73, 045322 (2006); PRBMDO 1098-0121 10.1103/PhysRevB.73.045322 (Pubitemid 43270648)
68. C. Wu, B.A. Bernevig, and S.-C. Zhang, Phys. Rev. Lett. 96, 106401 (2006). PRLTAO 0031-9007 10.1103/PhysRevLett.96.106401
69. A. Shitade, H. Katsura, J. Kuneš, X.-L. Qi, S.-C. Zhang, and N. Nagaosa, Phys. Rev. Lett. 102, 256403 (2009) PRLTAO 0031-9007 10.1103/PhysRevLett.102.256403
70. R. Roldán, E. Cappelluti, and F. Guinea, Phys. Rev. B 88, 054515 (2013). PRBMDO 1098-0121 10.1103/PhysRevB.88.054515