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Volumn 76, Issue 20, 2007, Pages

Tuning phase transition between quantum spin Hall and ordinary insulating phases

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EID: 35848931456     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.76.205304     Document Type: Article
Times cited : (209)

References (28)
  • 1
    • 0042972936 scopus 로고    scopus 로고
    • SCIEAS 0036-8075 10.1126/science.1087128
    • S. Murakami, N. Nagaosa, and S.-C. Zhang, Science SCIEAS 0036-8075 10.1126/science.1087128 301, 1348 (2003).
    • (2003) Science , vol.301 , pp. 1348
    • Murakami, S.1    Nagaosa, N.2    Zhang, S.-C.3
  • 3
    • 19644400795 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.93.156804
    • S. Murakami, N. Nagaosa, and S.-C. Zhang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.156804 93, 156804 (2004).
    • (2004) Phys. Rev. Lett. , vol.93 , pp. 156804
    • Murakami, S.1    Nagaosa, N.2    Zhang, S.-C.3
  • 4
    • 28844477210 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.95.146802
    • C. L. Kane and E. J. Mele, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.146802 95, 146802 (2005).
    • (2005) Phys. Rev. Lett. , vol.95 , pp. 146802
    • Kane, C.L.1    Mele, E.J.2
  • 5
    • 28844477796 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.95.226801
    • C. L. Kane and E. J. Mele, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.226801 95, 226801 (2005).
    • (2005) Phys. Rev. Lett. , vol.95 , pp. 226801
    • Kane, C.L.1    Mele, E.J.2
  • 6
    • 27144509118 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.95.106601
    • M. Onoda and N. Nagaosa, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.106601 95, 106601 (2005).
    • (2005) Phys. Rev. Lett. , vol.95 , pp. 106601
    • Onoda, M.1    Nagaosa, N.2
  • 7
    • 33644917486 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.96.106802
    • B. A. Bernevig and S.-C. Zhang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.106802 96, 106802 (2006).
    • (2006) Phys. Rev. Lett. , vol.96 , pp. 106802
    • Bernevig, B.A.1    Zhang, S.-C.2
  • 8
    • 33747116969 scopus 로고    scopus 로고
    • PRBMDO 0163-1829 10.1103/PhysRevB.74.085308
    • X.-L. Qi, Y.-S. Wu, and S.-C. Zhang, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.74.085308 74, 085308 (2006).
    • (2006) Phys. Rev. B , vol.74 , pp. 085308
    • Qi, X.-L.1    Wu, Y.-S.2    Zhang, S.-C.3
  • 10
    • 33947198126 scopus 로고    scopus 로고
    • PRBMDO 0163-1829 10.1103/PhysRevB.75.121403
    • T. Fukui and Y. Hatsugai, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.75.121403 75, 121403 (R) (2007).
    • (2007) Phys. Rev. B , vol.75 , pp. 121403
    • Fukui, T.1    Hatsugai, Y.2
  • 11
    • 33750926079 scopus 로고    scopus 로고
    • PRBMDO 0163-1829 10.1103/PhysRevB.74.195312
    • L. Fu and C. L. Kane, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.74. 195312 74, 195312 (2006).
    • (2006) Phys. Rev. B , vol.74 , pp. 195312
    • Fu, L.1    Kane, C.L.2
  • 12
    • 33847795859 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.98.106803
    • L. Fu, C. L. Kane, and E. J. Mele, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.106803 98, 106803 (2007).
    • (2007) Phys. Rev. Lett. , vol.98 , pp. 106803
    • Fu, L.1    Kane, C.L.2    Mele, E.J.3
  • 13
    • 34347373900 scopus 로고    scopus 로고
    • PRBMDO 0163-1829 10.1103/PhysRevB.76.045302
    • L. Fu and C. L. Kane, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.76. 045302 76, 045302 (2007).
    • (2007) Phys. Rev. B , vol.76 , pp. 045302
    • Fu, L.1    Kane, C.L.2
  • 14
    • 33845290260 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.97.236805
    • S. Murakami, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97. 236805 97, 236805 (2006).
    • (2006) Phys. Rev. Lett. , vol.97 , pp. 236805
    • Murakami, S.1
  • 15
    • 33847015684 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.98.076802
    • M. Onoda, Y. Avishai, and N. Nagaosa, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.076802 98, 076802 (2007).
    • (2007) Phys. Rev. Lett. , vol.98 , pp. 076802
    • Onoda, M.1    Avishai, Y.2    Nagaosa, N.3
  • 16
    • 33644910778 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.96.106401
    • C. Wu, B. A. Bernevig, and S.-C. Zhang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.106401 96, 106401 (2006).
    • (2006) Phys. Rev. Lett. , vol.96 , pp. 106401
    • Wu, C.1    Bernevig, B.A.2    Zhang, S.-C.3
  • 17
    • 33144489555 scopus 로고    scopus 로고
    • PRBMDO 0163-1829 10.1103/PhysRevB.73.045322
    • C. Xu and J. E. Moore, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.73. 045322 73, 045322 (2006).
    • (2006) Phys. Rev. B , vol.73 , pp. 045322
    • Xu, C.1    Moore, J.E.2
  • 18
    • 33845708953 scopus 로고    scopus 로고
    • SCIEAS 0036-8075 10.1126/science.1133734
    • B. A. Bernevig, T. L. Hughes, and S.-C. Zhang, Science SCIEAS 0036-8075 10.1126/science.1133734 314, 1757 (2006).
    • (2006) Science , vol.314 , pp. 1757
    • Bernevig, B.A.1    Hughes, T.L.2    Zhang, S.-C.3
  • 19
    • 34848853530 scopus 로고    scopus 로고
    • NJOPFM 1367-2630 10.1088/1367-2630/9/9/356
    • S. Murakami, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/9/9/356 9, 356 (2007).
    • (2007) New J. Phys. , vol.9 , pp. 356
    • Murakami, S.1
  • 20
    • 35848934010 scopus 로고    scopus 로고
    • The pseudospin α, which labels the eigenstates, is different from the spin in the presence of the spin-orbit coupling.
    • The pseudospin α, which labels the eigenstates, is different from the spin in the presence of the spin-orbit coupling.
  • 24
    • 35848966454 scopus 로고    scopus 로고
    • By considering all possible 2D magnetic point groups, we found some exceptional models with degeneracy at k = G /2, even without I symmetry. These cases result from a rather high symmetry of the system. It is expected that by including some perturbation to lower the symmetry the Hamiltonian will reduce to the case (a) in Fig. 1.
    • By considering all possible 2D magnetic point groups, we found some exceptional models with degeneracy at k = G /2, even without I symmetry. These cases result from a rather high symmetry of the system. It is expected that by including some perturbation to lower the symmetry the Hamiltonian will reduce to the case (a) in Fig. 1.
  • 25
    • 35848931773 scopus 로고    scopus 로고
    • In some exceptional cases with high point-group symmetry, the gap between two doubly degenerate bands can close even when k ≠ G /2. In 2D this occurs for the magnetic point-group symmetries 3̄ ′, 3̄ ′ m, 3̄ ′ m′, 6′ /m, 6′/m m′ m, which are in trigonal system or hexagonal systems. It is expected that the closing of the gap in these cases does not correspond to phase transition between the QSH and the SHI, as some perturbation can circumvent this degeneracy.
    • In some exceptional cases with high point-group symmetry, the gap between two doubly degenerate bands can close even when k ≠ G /2. In 2D this occurs for the magnetic point-group symmetries 3̄ ′, 3̄ ′ m, 3̄ ′ m′, 6′ /m, 6′ /m m′ m, which are in trigonal system or hexagonal systems. It is expected that the closing of the gap in these cases does not correspond to phase transition between the QSH and the SHI, as some perturbation can circumvent this degeneracy.
  • 26
    • 33947696243 scopus 로고    scopus 로고
    • PRBMDO 0163-1829 10.1103/PhysRevB.75.121306
    • J. E. Moore and L. Balents, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.75.121306 75, 121306 (R) (2007).
    • (2007) Phys. Rev. B , vol.75 , pp. 121306
    • Moore, J.E.1    Balents, L.2
  • 27
    • 33744778964 scopus 로고
    • A similar problem has been discussed in the context of fractional fermion number. See PRPLCM 0370-1573 10.1016/0370-1573(86)90167-5
    • A similar problem has been discussed in the context of fractional fermion number. See A. J. Niemi and G. W. Semenoff, Phys. Rep. PRPLCM 0370-1573 10.1016/0370-1573(86)90167-5 135, 99 (1986) for a review. A concrete example is the midgap state associated with dimerized soliton in polyacetylene as discussed in
    • (1986) Phys. Rep. , vol.135 , pp. 99
    • Niemi, A.J.1    Semenoff, G.W.2
  • 28


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.