SCOPUS 정보 검색 플랫폼

Physical Review Letters

Volumn 114, Issue 22, 2015, Pages

Topological Crystalline Insulator Phase in Graphene Multilayers

(1) Kindermann, M a

a GEORGIA INSTITUTE OF TECHNOLOGY (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CRYSTAL SYMMETRY; ELECTRIC INSULATORS; ENERGY GAP; GRAPHENE; MULTILAYERS; SEMICONDUCTOR QUANTUM WELLS; SEMICONDUCTOR QUANTUM WIRES;

CRYSTALLINE INSULATORS; GRAPHENE MULTILAYERS; LOW DISSIPATIONS; TOPOLOGICAL INSULATORS; TOPOLOGICAL PHASE; TOPOLOGICAL STATE;

TOPOLOGY;

EID: 84935880025 PISSN: 00319007 EISSN: 10797114 Source Type: Journal
DOI: 10.1103/PhysRevLett.114.226802 Document Type: Article

Times cited : (40)

References (57)

1
- 77949375457
- J.E. Moore, Nature (London) 464, 194 (2010). NATUAS 0028-0836 10.1038/nature08916
- (2010) Nature (London) , vol.464 , pp. 194
- Moore, E.J.¹

2
- 78349239882
- M.Z. Hasan and C.L. Kane, Rev. Mod. Phys. 82, 3045 (2010). RMPHAT 0034-6861 10.1103/RevModPhys.82.3045
- (2010) Rev. Mod. Phys. , vol.82 , pp. 3045
- Hasan, M.Z.¹ Kane, C.L.²

3
- 80054934761
- X.-L. Qi and S.-C. Zhang, Rev. Mod. Phys. 83, 1057 (2011). RMPHAT 0034-6861 10.1103/RevModPhys.83.1057
- (2011) Rev. Mod. Phys. , vol.83 , pp. 1057
- Qi, X.-L.¹ Zhang, S.-C.²

4
- 84864829856
- T.H. Hsieh, H. Lin, J. Liu, W. Duan, A. Bansil, and L. Fu, Nat. Commun. 3, 982 (2012). NCAOBW 2041-1723 10.1038/ncomms1969
- (2012) Nat. Commun. , vol.3 , pp. 982
- Hsieh, T.H.¹ Lin, H.² Liu, J.³ Duan, W.⁴ Bansil, A.⁵ Fu, L.⁶

5
- 84868681541
- Y. Tanaka, Z. Ren, T. Sato, K. Nakayama, S. Souma, T. Takahashi, K. Segawa, and Y. Ando, Nat. Phys. 8, 800 (2012). NPAHAX 1745-2473 10.1038/nphys2442
- (2012) Nat. Phys. , vol.8 , pp. 800
- Tanaka, Y.¹ Ren, Z.² Sato, T.³ Nakayama, K.⁴ Souma, S.⁵ Takahashi, T.⁶ Segawa, K.⁷ Ando, Y.⁸

6
- 84870037398
- P. Dziawa, B.J. Kowalski, K. Dybko, R. Buczko, A. Szczerbakow, M. Szot, E. Łusakowska, T. Balasubramanian, B.M. Wojek, M.H. Berntsen, Nat. Mater. 11, 1023 (2012). NMAACR 1476-1122
- (2012) Nat. Mater. , vol.11 , pp. 1023
- Dziawa, P.¹ Kowalski, B.J.² Dybko, K.³ Buczko, R.⁴ Szczerbakow, A.⁵ Szot, M.⁶ Łusakowska, E.⁷ Balasubramanian, T.⁸ Wojek, B.M.⁹ Berntsen, M.H.¹⁰

7
- 84935841492
- arXiv:1206.2088
- S.-Y. Xu, C. Liu, N. Alidoust, D. Qian, M. Neupane, J.D. Denlinger, Y.J. Wang, L.A. Wray, R.J. Cava, H. Lin, arXiv:1206.2088.
- Xu, S.-Y.¹ Liu, C.² Alidoust, N.³ Qian, D.⁴ Neupane, M.⁵ Denlinger, J.D.⁶ Wang, Y.J.⁷ Wray, L.A.⁸ Cava, R.J.⁹ Lin, H.¹⁰

8
- 84883312952
- H. Yao and S. Ryu, Phys. Rev. B 88, 064507 (2013). PRBMDO 1098-0121 10.1103/PhysRevB.88.064507
- (2013) Phys. Rev. B , vol.88 , pp. 064507
- Yao, H.¹ Ryu, S.²

9
- 84870856778
- S.-Y. Xu, C. Liu, N. Alidoust, M. Neupane, D. Qian, I. Belopolski, J.D. Denlinger, Y.J. Wang, H. Lin, L.A. Wray, Nat. Commun. 3, 1192 (2012). NCAOBW 2041-1723 10.1038/ncomms2191
- (2012) Nat. Commun. , vol.3 , pp. 1192
- Xu, S.-Y.¹ Liu, C.² Alidoust, N.³ Neupane, M.⁴ Qian, D.⁵ Belopolski, I.⁶ Denlinger, J.D.⁷ Wang, Y.J.⁸ Lin, H.⁹ Wray, L.A.¹⁰

10
- 84881510955
- F. Zhang, C.L. Kane, and E.J. Mele, Phys. Rev. Lett. 111, 056403 (2013). PRLTAO 0031-9007 10.1103/PhysRevLett.111.056403
- (2013) Phys. Rev. Lett. , vol.111 , pp. 056403
- Zhang, F.¹ Kane, C.L.² Mele, E.J.³

11
- 84924405539
- Y. Ando and L. Fu, Annu. Rev. Condens. Matter Phys. 6, 361 (2015). ARCMCX 1947-5454 10.1146/annurev-conmatphys-031214-014501
- (2015) Annu. Rev. Condens. Matter Phys. , vol.6 , pp. 361
- Ando, Y.¹ Fu, L.²

12
- 79952420794
- L. Fu, Phys. Rev. Lett. 106, 106802 (2011). PRLTAO 0031-9007 10.1103/PhysRevLett.106.106802
- (2011) Phys. Rev. Lett. , vol.106 , pp. 106802
- Fu, L.¹

13
- 84873409812
- R.-J. Slager, A. Mesaros, V. Juricic, and J. Zaanen, Nat. Phys. 9, 98 (2013). NPAHAX 1745-2473 10.1038/nphys2513
- (2013) Nat. Phys. , vol.9 , pp. 98
- Slager, R.-J.¹ Mesaros, A.² Juricic, V.³ Zaanen, J.⁴

14
- 28844477796
- C.L. Kane and E.J. Mele, Phys. Rev. Lett. 95, 226801 (2005). PRLTAO 0031-9007 10.1103/PhysRevLett.95.226801
- (2005) Phys. Rev. Lett. , vol.95 , pp. 226801
- Kane, C.L.¹ Mele, E.J.²

15
- 28844477210
- C.L. Kane and E.J. Mele, Phys. Rev. Lett. 95, 146802 (2005). PRLTAO 0031-9007 10.1103/PhysRevLett.95.146802
- (2005) Phys. Rev. Lett. , vol.95 , pp. 146802
- Kane, C.L.¹ Mele, E.J.²

16
- 33845708953
- B.A. Bernevig, T.L. Hughes, and S.-C. Zhang, Science 314, 1757 (2006). SCIEAS 0036-8075 10.1126/science.1133734
- (2006) Science , vol.314 , pp. 1757
- Bernevig, B.A.¹ Hughes, T.L.² Zhang, S.-C.³

17
- 45249103494
- C. Liu, T.L. Hughes, X.-L. Qi, K. Wang, and S.-C. Zhang, Phys. Rev. Lett. 100, 236601 (2008). PRLTAO 0031-9007 10.1103/PhysRevLett.100.236601
- (2008) Phys. Rev. Lett. , vol.100 , pp. 236601
- Liu, C.¹ Hughes, T.L.² Qi, X.-L.³ Wang, K.⁴ Zhang, S.-C.⁵

18
- 33845290260
- S. Murakami, Phys. Rev. Lett. 97, 236805 (2006). PRLTAO 0031-9007 10.1103/PhysRevLett.97.236805
- (2006) Phys. Rev. Lett. , vol.97 , pp. 236805
- Murakami, S.¹

19
- 84455194882
- D. Xiao, W. Zhu, Y. Ran, N. Nagaosa, and S. Okamoto, Nat. Commun. 2, 596 (2011). NCAOBW 2041-1723 10.1038/ncomms1602
- (2011) Nat. Commun. , vol.2 , pp. 596
- Xiao, D.¹ Zhu, W.² Ran, Y.³ Nagaosa, N.⁴ Okamoto, S.⁵

20
- 84870233097
- P. Ghaemi, S. Gopalakrishnan, and T.L. Hughes, Phys. Rev. B 86, 201406 (2012). PRBMDO 1098-0121 10.1103/PhysRevB.86.201406
- (2012) Phys. Rev. B , vol.86 , pp. 201406
- Ghaemi, P.¹ Gopalakrishnan, S.² Hughes, T.L.³

21
- 38949129028
- 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
- (2007) Science , vol.318 , pp. 766
- König, M.¹ Wiedmann, S.² Brüne, C.³ Roth, A.⁴ Buhmann, H.⁵ Molenkamp, L.W.⁶ Qi, X.-L.⁷ Zhang, S.-C.⁸

22
- 80053117994
- I. Knez, R.-R. Du, and G. Sullivan, Phys. Rev. Lett. 107, 136603 (2011). PRLTAO 0031-9007 10.1103/PhysRevLett.107.136603
- (2011) Phys. Rev. Lett. , vol.107 , pp. 136603
- Knez, I.¹ Du, R.-R.² Sullivan, G.³

23
- 33846457928
- Y. Yao, F. Ye, X.-L. Qi, S.-C. Zhang, and Z. Fang, Phys. Rev. B 75, 041401 (2007). PRBMDO 1098-0121 10.1103/PhysRevB.75.041401
- (2007) Phys. Rev. B , vol.75 , pp. 041401
- Yao, Y.¹ Ye, F.² Qi, X.-L.³ Zhang, S.-C.⁴ Fang, Z.⁵

24
- 33947167338
- J.C. Boettger and S.B. Trickey, Phys. Rev. B 75, 121402 (2007). PRBMDO 1098-0121 10.1103/PhysRevB.75.121402
- (2007) Phys. Rev. B , vol.75 , pp. 121402
- Boettger, J.C.¹ Trickey, S.B.²

25
- 42249099225
- S. Raghu, X.-L. Qi, C. Honerkamp, and S.-C. Zhang, Phys. Rev. Lett. 100, 156401 (2008). PRLTAO 0031-9007 10.1103/PhysRevLett.100.156401
- (2008) Phys. Rev. Lett. , vol.100 , pp. 156401
- Raghu, S.¹ Qi, X.-L.² Honerkamp, C.³ Zhang, S.-C.⁴

26
- 77954871877
- C. Weeks and M. Franz, Phys. Rev. B 81, 085105 (2010). PRBMDO 1098-0121 10.1103/PhysRevB.81.085105
- (2010) Phys. Rev. B , vol.81 , pp. 085105
- Weeks, C.¹ Franz, M.²

27
- 79960624487
- F. Zhang, J. Jung, G.A. Fiete, Q. Niu, and A.H. MacDonald, Phys. Rev. Lett. 106, 156801 (2011). PRLTAO 0031-9007 10.1103/PhysRevLett.106.156801
- (2011) Phys. Rev. Lett. , vol.106 , pp. 156801
- Zhang, F.¹ Jung, J.² Fiete, G.A.³ Niu, Q.⁴ Macdonald, A.H.⁵

28
- 84857771680
- T. Pereg-Barnea and G. Refael, Phys. Rev. B 85, 075127 (2012). PRBMDO 1098-0121 10.1103/PhysRevB.85.075127
- (2012) Phys. Rev. B , vol.85 , pp. 075127
- Pereg-Barnea, T.¹ Refael, G.²

29
- 79957997633
- N.H. Lindner, G. Refael, and V. Galitski, Nat. Phys. 7, 490 (2011). NPAHAX 1745-2473 10.1038/nphys1926
- (2011) Nat. Phys. , vol.7 , pp. 490
- Lindner, N.H.¹ Refael, G.² Galitski, V.³

30
- 54849435714
- A. Varykhalov, J. Sánchez-Barriga, A.M. Shikin, C. Biswas, E. Vescovo, A. Rybkin, D. Marchenko, and O. Rader, Phys. Rev. Lett. 101, 157601 (2008). PRLTAO 0031-9007 10.1103/PhysRevLett.101.157601
- (2008) Phys. Rev. Lett. , vol.101 , pp. 157601
- Varykhalov, A.¹ Sánchez-Barriga, J.² Shikin, A.M.³ Biswas, C.⁴ Vescovo, E.⁵ Rybkin, A.⁶ Marchenko, D.⁷ Rader, O.⁸

31
- 68849129290
- A.H.C. Neto and F. Guinea, Phys. Rev. Lett. 103, 026804 (2009). PRLTAO 0031-9007 10.1103/PhysRevLett.103.026804
- (2009) Phys. Rev. Lett. , vol.103 , pp. 026804
- Neto, A.H.C.¹ Guinea, F.²

32
- 77957748095
- S. Abdelouahed, A. Ernst, J. Henk, I.V. Maznichenko, and I. Mertig, Phys. Rev. B 82, 125424 (2010). PRBMDO 1098-0121 10.1103/PhysRevB.82.125424
- (2010) Phys. Rev. B , vol.82 , pp. 125424
- Abdelouahed, S.¹ Ernst, A.² Henk, J.³ Maznichenko, I.V.⁴ Mertig, I.⁵

33
- 82655173513
- 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
- (2011) Phys. Rev. X , vol.1 , pp. 021001
- Weeks, C.¹ Hu, J.² Alicea, J.³ Franz, M.⁴ Wu, R.⁵

34
- 83655193084
- Z. Qiao, W.-K. Tse, H. Jiang, Y. Yao, and Q. Niu, Phys. Rev. Lett. 107, 256801 (2011). PRLTAO 0031-9007 10.1103/PhysRevLett.107.256801
- (2011) Phys. Rev. Lett. , vol.107 , pp. 256801
- Qiao, Z.¹ Tse, W.-K.² Jiang, H.³ Yao, Y.⁴ Niu, Q.⁵

35
- 84866318134
- H. Jiang, Z. Qiao, H. Liu, J. Shi, and Q. Niu, Phys. Rev. Lett. 109, 116803 (2012). PRLTAO 0031-9007 10.1103/PhysRevLett.109.116803
- (2012) Phys. Rev. Lett. , vol.109 , pp. 116803
- Jiang, H.¹ Qiao, Z.² Liu, H.³ Shi, J.⁴ Niu, Q.⁵

36
- 84871754747
- J. Hu, J. Alicea, R. Wu, and M. Franz, Phys. Rev. Lett. 109, 266801 (2012). PRLTAO 0031-9007 10.1103/PhysRevLett.109.266801
- (2012) Phys. Rev. Lett. , vol.109 , pp. 266801
- Hu, J.¹ Alicea, J.² Wu, R.³ Franz, M.⁴

37
- 84874903301
- Z. Qiao, X. Li, W.-K. Tse, H. Jiang, Y. Yao, and Q. Niu, Phys. Rev. B 87, 125405 (2013). PRBMDO 1098-0121 10.1103/PhysRevB.87.125405
- (2013) Phys. Rev. B , vol.87 , pp. 125405
- Qiao, Z.¹ Li, X.² Tse, W.-K.³ Jiang, H.⁴ Yao, Y.⁵ Niu, Q.⁶

38
- 77955384187
- E.J. Mele, Phys. Rev. B 81, 161405 (2010). PRBMDO 1098-0121 10.1103/PhysRevB.81.161405
- (2010) Phys. Rev. B , vol.81 , pp. 161405
- Mele, J.E.¹

39
- 49149123931
- S. Shallcross, S. Sharma, and O.A. Pankratov, Phys. Rev. Lett. 101, 056803 (2008). PRLTAO 0031-9007 10.1103/PhysRevLett.101.056803
- (2008) Phys. Rev. Lett. , vol.101 , pp. 056803
- Shallcross, S.¹ Sharma, S.² Pankratov, O.A.³

40
- 84999354211
- At high energies there are additional interlayer coupling terms that do not conserve the "Dirac" momentum (Equation presented) that appears in Eq. (1) [57]. At the (large) interlayer rotation angles of interest here, however, these terms merely renormalize the carrier velocity (Equation presented) [57] in the low-energy theory Eq. (1) and they thus do not appear explicitly
- At high energies there are additional interlayer coupling terms that do not conserve the "Dirac" momentum (Equation presented) that appears in Eq. (1) [57]. At the (large) interlayer rotation angles of interest here, however, these terms merely renormalize the carrier velocity (Equation presented) [57] in the low-energy theory Eq. (1) and they thus do not appear explicitly.

41
- 59949098337
- A.H.C. Neto, F. Guinea, N.M.R. Peres, K.S. Novoselov, and A.K. Geim, Rev. Mod. Phys. 81, 109 (2009). RMPHAT 0034-6861 10.1103/RevModPhys.81.109
- (2009) Rev. Mod. Phys. , vol.81 , pp. 109
- Neto, A.H.C.¹ Guinea, F.² Peres, N.M.R.³ Novoselov, K.S.⁴ Geim, A.K.⁵

42
- 84884470703
- C.-K. Chiu, H. Yao, and S. Ryu, Phys. Rev. B 88, 075142 (2013). PRBMDO 1098-0121 10.1103/PhysRevB.88.075142
- (2013) Phys. Rev. B , vol.88 , pp. 075142
- Chiu, C.-K.¹ Yao, H.² Ryu, S.³

43
- 4043108064
- S. Reich, J. Maultzsch, C. Thomsen, and P. Ordejón, Phys. Rev. B 66, 035412 (2002). PRBMDO 0163-1829 10.1103/PhysRevB.66.035412
- (2002) Phys. Rev. B , vol.66 , pp. 035412
- Reich, S.¹ Maultzsch, J.² Thomsen, C.³ Ordejón, P.⁴

44
- 80053915919
- A.M. Essin and V. Gurarie, Phys. Rev. B 84, 125132 (2011). PRBMDO 1098-0121 10.1103/PhysRevB.84.125132
- (2011) Phys. Rev. B , vol.84 , pp. 125132
- Essin, A.M.¹ Gurarie, V.²

45
- 84935844739
- See Supplemental Material at for a discussion of the topological invariant in the low-energy model
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevLett.114.226802 for a discussion of the topological invariant in the low-energy model.

46
- 4244059763
- E.J. Weinberg, Phys. Rev. D 24, 2669 (1981). PRVDAQ 0556-2821 10.1103/PhysRevD.24.2669
- (1981) Phys. Rev. D , vol.24 , pp. 2669
- Weinberg, J.E.¹

47
- 84922215868
- (Clarendon, Oxford), Chap. 22
- G.E. Volovik, The Universe in a Helium Droplet (Clarendon, Oxford, 2003), Chap. 22.
- (2003) The Universe in A Helium Droplet
- Volovik, E.G.¹

48
- 84935914208
- Pairs of boundary modes with opposite (Equation presented) eigenvalues evidently do not contribute to (Equation presented) and can increase the number of boundary modes above (Equation presented)
- Pairs of boundary modes with opposite (Equation presented) eigenvalues evidently do not contribute to (Equation presented) and can increase the number of boundary modes above (Equation presented).

49
- 19944428003
- C. Berger, Z. Song, T. Li, X. Li, A.Y. Ogbazghi, R. Feng, Z. Dai, A.N. Marchenkov, E.H. Conrad, P.N. First, J. Phys. Chem. B 108, 19912 (2004). JPCBFK 1520-6106 10.1021/jp040650f
- (2004) J. Phys. Chem. B , vol.108 , pp. 19912
- Berger, C.¹ Song, Z.² Li, T.³ Li, X.⁴ Ogbazghi, A.Y.⁵ Feng, R.⁶ Dai, Z.⁷ Marchenkov, A.N.⁸ Conrad, E.H.⁹ First, P.N.¹⁰

50
- 84866555047
- W. Yan, M. Liu, R.-F. Dou, L. Meng, L. Feng, Z.-D. Chu, Y. Zhang, Z. Liu, J.-C. Nie, and L. He, Phys. Rev. Lett. 109, 126801 (2012). PRLTAO 0031-9007 10.1103/PhysRevLett.109.126801
- (2012) Phys. Rev. Lett. , vol.109 , pp. 126801
- Yan, W.¹ Liu, M.² Dou, R.-F.³ Meng, L.⁴ Feng, L.⁵ Chu, Z.-D.⁶ Zhang, Y.⁷ Liu, Z.⁸ Nie, J.-C.⁹ He, L.¹⁰

51
- 84856870160
- J.D. Sanchez-Yamagishi, T. Taychatanapat, K. Watanabe, T. Taniguchi, A. Yacoby, and P. Jarillo-Herrero, Phys. Rev. Lett. 108, 076601 (2012). PRLTAO 0031-9007 10.1103/PhysRevLett.108.076601
- (2012) Phys. Rev. Lett. , vol.108 , pp. 076601
- Sanchez-Yamagishi, J.D.¹ Taychatanapat, T.² Watanabe, K.³ Taniguchi, T.⁴ Yacoby, A.⁵ Jarillo-Herrero, P.⁶

52
- 84935911422
- arXiv:1409.1971
- H.K. Pal, S. Carter, and M. Kindermann, arXiv:1409.1971.
- Pal, H.K.¹ Carter, S.² Kindermann, M.³

53
- 84999334374
- In a graphene bilayer rotated by angle (Equation presented) from a commensurate angle (Equation presented), regions with size of the order (Equation presented) appear, that have approximately SE-even stacking. There, the described topological modes can be observed if their spatial extent (Equation presented) is smaller than those regions. For (Equation presented) with (Equation presented) [39] this is fulfilled when (Equation presented)
- In a graphene bilayer rotated by angle (Equation presented) from a commensurate angle (Equation presented), regions with size of the order (Equation presented) appear, that have approximately SE-even stacking. There, the described topological modes can be observed if their spatial extent (Equation presented) is smaller than those regions. For (Equation presented) with (Equation presented) [39] this is fulfilled when (Equation presented).

54
- 84915775124
- A. Mishchenko, J.S. Tu, Y. Cao, R.V. Gorbachev, J.R. Wallbank, M.T. Greenaway, V.E. Morozov, S.V. Morozov, M.J. Zhu, S.L. Wong, Nat. Nanotechnol. 9, 808 (2014). NNAABX 1748-3387 10.1038/nnano.2014.187
- (2014) Nat. Nanotechnol. , vol.9 , pp. 808
- Mishchenko, A.¹ Tu, J.S.² Cao, Y.³ Gorbachev, R.V.⁴ Wallbank, J.R.⁵ Greenaway, M.T.⁶ Morozov, V.E.⁷ Morozov, S.V.⁸ Zhu, M.J.⁹ Wong, S.L.¹⁰

55
- 78651289499
- J. Li, A.F. Morpurgo, M. Büttiker, and I. Martin, Phys. Rev. B 82, 245404 (2010). PRBMDO 1098-0121 10.1103/PhysRevB.82.245404
- (2010) Phys. Rev. B , vol.82 , pp. 245404
- Li, J.¹ Morpurgo, A.F.² Büttiker, M.³ Martin, I.⁴

56
- 38549107031
- I. Martin, Y.M. Blanter, and A.F. Morpurgo, Phys. Rev. Lett. 100, 036804 (2008). PRLTAO 0031-9007 10.1103/PhysRevLett.100.036804
- (2008) Phys. Rev. Lett. , vol.100 , pp. 036804
- Martin, I.¹ Blanter, Y.M.² Morpurgo, A.F.³

57
- 37249024663
- J.M.B. Lopes dos Santos, N.M.R. Peres, and A.H. Castro Neto, Phys. Rev. Lett. 99, 256802 (2007). PRLTAO 0031-9007 10.1103/PhysRevLett.99.256802
- (2007) Phys. Rev. Lett. , vol.99 , pp. 256802
- Lopes Dos Santos, J.M.B.¹ Peres, N.M.R.² Castro Neto, A.H.³

* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.