메뉴 건너뛰기




Volumn 90, Issue 2, 2014, Pages

Topological Blount's theorem of odd-parity superconductors

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84904994437     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.90.024516     Document Type: Article
Times cited : (143)

References (55)
  • 1
    • 35949031127 scopus 로고
    • RMPHAT 0034-6861 10.1103/RevModPhys.47.331
    • A. J. Legget, Rev. Mod. Phys. 47, 331 (1975). RMPHAT 0034-6861 10.1103/RevModPhys.47.331
    • (1975) Rev. Mod. Phys. , vol.47 , pp. 331
    • Legget, A.J.1
  • 2
    • 0345704681 scopus 로고
    • RMPHAT 0034-6861 10.1103/RevModPhys.63.239
    • M. Sigrist and K. Ueda, Rev. Mod. Phys. 63, 239 (1991). RMPHAT 0034-6861 10.1103/RevModPhys.63.239
    • (1991) Rev. Mod. Phys. , vol.63 , pp. 239
    • Sigrist, M.1    Ueda, K.2
  • 3
    • 0001619823 scopus 로고
    • PRBMDO 0163-1829 10.1103/PhysRevB.32.2935
    • E. I. Blount, Phys. Rev. B 32, 2935 (1985). PRBMDO 0163-1829 10.1103/PhysRevB.32.2935
    • (1985) Phys. Rev. B , vol.32 , pp. 2935
    • Blount, E.I.1
  • 4
    • 0035993873 scopus 로고    scopus 로고
    • RMPHAT 0034-6861 10.1103/RevModPhys.74.235
    • R. Joynt and L. Taillefer, Rev. Mod. Phys. 74, 235 (2002). RMPHAT 0034-6861 10.1103/RevModPhys.74.235
    • (2002) Rev. Mod. Phys. , vol.74 , pp. 235
    • Joynt, R.1    Taillefer, L.2
  • 5
    • 0038035702 scopus 로고    scopus 로고
    • JUPSAU 0031-9015 10.1143/JPSJ.72.673
    • Y. Yanase and M. Ogata, J. Phys. Soc. Jpn. 72, 673 (2003). JUPSAU 0031-9015 10.1143/JPSJ.72.673
    • (2003) J. Phys. Soc. Jpn. , vol.72 , pp. 673
    • Yanase, Y.1    Ogata, M.2
  • 6
    • 33744936028 scopus 로고    scopus 로고
    • Nodal structure of superconductors with time-reversal invariance and Z2 topological number
    • DOI 10.1103/PhysRevB.73.214502
    • M. Sato, Phys. Rev. B 73, 214502 (2006). PRBMDO 1098-0121 10.1103/PhysRevB.73.214502 (Pubitemid 43848237)
    • (2006) Physical Review B - Condensed Matter and Materials Physics , vol.73 , Issue.21 , pp. 214502
    • Sato, M.1
  • 7
    • 77955210446 scopus 로고    scopus 로고
    • PRBMDO 1098-0121 10.1103/PhysRevB.81.134515
    • B. Béri, Phys. Rev. B 81, 134515 (2010). PRBMDO 1098-0121 10.1103/PhysRevB.81.134515
    • (2010) Phys. Rev. B , vol.81 , pp. 134515
    • Béri, B.1
  • 9
    • 27144492596 scopus 로고    scopus 로고
    • Stability of fermi surfaces and K theory
    • DOI 10.1103/PhysRevLett.95.016405, 016405
    • P. Hořava, Phys. Rev Lett. 95, 016405 (2005). PRLTAO 0031-9007 10.1103/PhysRevLett.95.016405 (Pubitemid 41506384)
    • (2005) Physical Review Letters , vol.95 , Issue.1 , pp. 1-4
    • Horava, P.1
  • 10
    • 84879098260 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.110.240404
    • Y. X. Zhao and Z. D. Wang, Phys. Rev. Lett. 110, 240404 (2013). PRLTAO 0031-9007 10.1103/PhysRevLett.110.240404
    • (2013) Phys. Rev. Lett. , vol.110 , pp. 240404
    • Zhao, Y.X.1    Wang, Z.D.2
  • 11
    • 79961116179 scopus 로고    scopus 로고
    • PRBMDO 1098-0121 10.1103/PhysRevB.83.224511
    • M. Sato, Y. Tanaka, K. Yada, and T. Yokoyama, Phys. Rev. B 83, 224511 (2011). PRBMDO 1098-0121 10.1103/PhysRevB.83.224511
    • (2011) Phys. Rev. B , vol.83 , pp. 224511
    • Sato, M.1    Tanaka, Y.2    Yada, K.3    Yokoyama, T.4
  • 12
    • 79961076747 scopus 로고    scopus 로고
    • PRBMDO 1098-0121 10.1103/PhysRevB.83.064505
    • K. Yada, M. Sato, Y. Tanaka, and T. Yokoyama, Phys. Rev. B 83, 064505 (2011). PRBMDO 1098-0121 10.1103/PhysRevB.83.064505
    • (2011) Phys. Rev. B , vol.83 , pp. 064505
    • Yada, K.1    Sato, M.2    Tanaka, Y.3    Yokoyama, T.4
  • 13
    • 84855259719 scopus 로고    scopus 로고
    • JUPSAU 0031-9015 10.1143/JPSJ.81.011013
    • Y. Tanaka, M. Sato, and N. Nagaosa, J. Phys. Soc. Jpn. 81, 011013 (2012). JUPSAU 0031-9015 10.1143/JPSJ.81.011013
    • (2012) J. Phys. Soc. Jpn. , vol.81 , pp. 011013
    • Tanaka, Y.1    Sato, M.2    Nagaosa, N.3
  • 14
    • 80052365703 scopus 로고    scopus 로고
    • (R). PRBMDO 1098-0121 10.1103/PhysRevB.84.060504
    • A. P. Schnyder and S. Ryu, Phys. Rev. B 84, 060504 (R) (2011). PRBMDO 1098-0121 10.1103/PhysRevB.84.060504
    • (2011) Phys. Rev. B , vol.84 , pp. 060504
    • Schnyder, A.P.1    Ryu, S.2
  • 15
    • 79961197905 scopus 로고    scopus 로고
    • (R). PRBMDO 1098-0121 10.1103/PhysRevB.84.020501
    • P. M. R. Brydon, A. P. Schnyder, and C. Timm, Phys. Rev. B 84, 020501 (R) (2011). PRBMDO 1098-0121 10.1103/PhysRevB.84.020501
    • (2011) Phys. Rev. B , vol.84 , pp. 020501
    • Brydon, P.M.R.1    Schnyder, A.P.2    Timm, C.3
  • 16
    • 84856415274 scopus 로고    scopus 로고
    • PRBMDO 1098-0121 10.1103/PhysRevB.85.024522
    • A. P. Schnyder, P. M. R. Brydon, and C. Timm, Phys. Rev. B 85, 024522 (2012). PRBMDO 1098-0121 10.1103/PhysRevB.85.024522
    • (2012) Phys. Rev. B , vol.85 , pp. 024522
    • Schnyder, A.P.1    Brydon, P.M.R.2    Timm, C.3
  • 17
    • 84882565536 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.111.077001
    • A. P. Schnyder, C. Timm, and P. M. R. Brydon, Phys. Rev. Lett. 111, 077001 (2013). PRLTAO 0031-9007 10.1103/PhysRevLett.111.077001
    • (2013) Phys. Rev. Lett. , vol.111 , pp. 077001
    • Schnyder, A.P.1    Timm, C.2    Brydon, P.M.R.3
  • 19
    • 23044491349 scopus 로고
    • 0040-9383 10.1016/0040-9383(64)90003-5
    • M. F. Atiyah, R. Bott, and A. Shapiro, Topology 3, 3 (1964). 0040-9383 10.1016/0040-9383(64)90003-5
    • (1964) Topology , vol.3 , pp. 3
    • Atiyah, M.F.1    Bott, R.2    Shapiro, A.3
  • 21
    • 77955932339 scopus 로고    scopus 로고
    • (R). PRBMDO 1098-0121 10.1103/PhysRevB.81.220504
    • M. Sato, Phys. Rev. B 81, 220504 (R) (2010). PRBMDO 1098-0121 10.1103/PhysRevB.81.220504
    • (2010) Phys. Rev. B , vol.81 , pp. 220504
    • Sato, M.1
  • 22
    • 84905021086 scopus 로고    scopus 로고
    • We subtract the constant term from (Equation presented) and choose an appropriate basis, making (Equation presented) an irreducible matrix. Also, when dim(Equation presented), our classification is applicable only in the stable regime (Equation presented) for the complex case (Equation presented) and (Equation presented) for the real case (Equation presented).
    • We subtract the constant term from (Equation presented) and choose an appropriate basis, making (Equation presented) an irreducible matrix. Also, when dim(Equation presented), our classification is applicable only in the stable regime (Equation presented) for the complex case (Equation presented) and (Equation presented) for the real case (Equation presented).
  • 24
    • 0030515852 scopus 로고    scopus 로고
    • JMAPAQ 0022-2488 10.1063/1.531675
    • M. Zirnbauer, J. Math. Phys. 37, 4986 (1996). JMAPAQ 0022-2488 10.1063/1.531675
    • (1996) J. Math. Phys. , vol.37 , pp. 4986
    • Zirnbauer, M.1
  • 25
    • 0000023684 scopus 로고    scopus 로고
    • PRBMDO 0163-1829 10.1103/PhysRevB.55.1142
    • A. Altland and M. R. Zirnbauer, Phys. Rev. B 55, 1142 (1997). PRBMDO 0163-1829 10.1103/PhysRevB.55.1142
    • (1997) Phys. Rev. B , vol.55 , pp. 1142
    • Altland, A.1    Zirnbauer, M.R.2
  • 26
    • 84897658504 scopus 로고    scopus 로고
    • PRBMDO 0163-1829 10.1103/PhysRevB.89.075111
    • Y. X. Zhao and Z. D. Wang, Phys. Rev. B 89, 075111 (2013). PRBMDO 0163-1829 10.1103/PhysRevB.89.075111
    • (2013) Phys. Rev. B , vol.89 , pp. 075111
    • Zhao, Y.X.1    Wang, Z.D.2
  • 27
    • 65649108305 scopus 로고    scopus 로고
    • 10.1063/1.3149495
    • A. Kitaev, AIP Conf. Proc. 1134, 22 (2009). 10.1063/1.3149495
    • (2009) AIP Conf. Proc. , vol.1134 , pp. 22
    • Kitaev, A.1
  • 30
    • 84884854728 scopus 로고    scopus 로고
    • PRBMDO 1098-0121 10.1103/PhysRevB.88.125129
    • T. Morimoto and A. Furusaki, Phys. Rev. B 88, 125129 (2013). PRBMDO 1098-0121 10.1103/PhysRevB.88.125129
    • (2013) Phys. Rev. B , vol.88 , pp. 125129
    • Morimoto, T.1    Furusaki, A.2
  • 31
    • 84857761838 scopus 로고    scopus 로고
    • PRBMDO 1098-0121 10.1103/PhysRevB.85.085103
    • X.-G. Wen, Phys. Rev. B 85, 085103 (2012). PRBMDO 1098-0121 10.1103/PhysRevB.85.085103
    • (2012) Phys. Rev. B , vol.85 , pp. 085103
    • Wen, X.-G.1
  • 33
    • 26944494061 scopus 로고    scopus 로고
    • Evidence for line nodes in the superconducting energy gap of noncentrosymmetric CePt3Si from magnetic penetration depth measurements
    • DOI 10.1103/PhysRevLett.94.207002, 207002
    • I. Bonalde, W. Bramer-Escamilla, and E. Bauer, Phys. Rev. Lett. 94, 207002 (2005). PRLTAO 0031-9007 10.1103/PhysRevLett.94.207002 (Pubitemid 41481106)
    • (2005) Physical Review Letters , vol.94 , Issue.20 , pp. 1-4
    • Bonalde, I.1    Bramer-Escamilla, W.2    Bauer, E.3
  • 34
    • 0038300829 scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.72.1526
    • C. R. Hu, Phys. Rev. Lett. 72, 1526 (1994). PRLTAO 0031-9007 10.1103/PhysRevLett.72.1526
    • (1994) Phys. Rev. Lett. , vol.72 , pp. 1526
    • Hu, C.R.1
  • 35
    • 11944251829 scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.74.3451
    • Y. Tanaka and S. Kashiwaya, Phys. Rev. Lett. 74, 3451 (1995). PRLTAO 0031-9007 10.1103/PhysRevLett.74.3451
    • (1995) Phys. Rev. Lett. , vol.74 , pp. 3451
    • Tanaka, Y.1    Kashiwaya, S.2
  • 36
    • 0033753629 scopus 로고    scopus 로고
    • RPPHAG 0034-4885 10.1088/0034-4885/63/10/202
    • S. Kashiwaya and Y. Tanaka, Rep. Prog. Phys. 63, 1641 (2000). RPPHAG 0034-4885 10.1088/0034-4885/63/10/202
    • (2000) Rep. Prog. Phys. , vol.63 , pp. 1641
    • Kashiwaya, S.1    Tanaka, Y.2
  • 37
    • 84905021087 scopus 로고    scopus 로고
    • For the (Equation presented) class, the reflection symmetry satisfies (Equation presented) on the reflection plane, namely, (Equation presented) is block diagonalized by an eigenvalue of the reflection symmetry and each sector does not have PHS. The absence of PHS in the sector implies that the stability of the line node is directly determined by that of the Fermi surface intersecting with the reflection plane. In fact, the reflection sector belongs to the topologically nontrivial state of the A class in the AZ classes. Similarly, for the (Equation presented) case, the commutation relations are given by (Equation presented). Hence PHS also breaks in the reflection sector, but the TRS remains in each sector, i.e., the reflection sector belongs to the AII class of the AZ classes.
    • For the (Equation presented) class, the reflection symmetry satisfies (Equation presented) on the reflection plane, namely, (Equation presented) is block diagonalized by an eigenvalue of the reflection symmetry and each sector does not have PHS. The absence of PHS in the sector implies that the stability of the line node is directly determined by that of the Fermi surface intersecting with the reflection plane. In fact, the reflection sector belongs to the topologically nontrivial state of the A class in the AZ classes. Similarly, for the (Equation presented) case, the commutation relations are given by (Equation presented). Hence PHS also breaks in the reflection sector, but the TRS remains in each sector, i.e., the reflection sector belongs to the AII class of the AZ classes.
  • 38
    • 84905047054 scopus 로고    scopus 로고
    • (Equation presented)-SRS is equivalent with (Equation presented)-SRS around a quantization axis in the mean-field level. We choose the (Equation presented)-SRS as a sufficient condition of SRS, since (Equation presented)-SRS is a looser condition than (Equation presented)-SRS.
    • (Equation presented)-SRS is equivalent with (Equation presented)-SRS around a quantization axis in the mean-field level. We choose the (Equation presented)-SRS as a sufficient condition of SRS, since (Equation presented)-SRS is a looser condition than (Equation presented)-SRS.
  • 39
    • 84905021083 scopus 로고    scopus 로고
    • For the (Equation presented) state of (Equation presented) B phase, provided that (Equation presented), the line node is protected by the mirror reflection (Equation presented) and the SRS (Equation presented). This is proved as follows. The combined operator (Equation presented) gives a new reflection operator satisfying (Equation presented) and (Equation presented). Thus (Equation presented) belongs to the (Equation presented) class, which has a stable line node.
    • For the (Equation presented) state of (Equation presented) B phase, provided that (Equation presented), the line node is protected by the mirror reflection (Equation presented) and the SRS (Equation presented). This is proved as follows. The combined operator (Equation presented) gives a new reflection operator satisfying (Equation presented) and (Equation presented). Thus (Equation presented) belongs to the (Equation presented) class, which has a stable line node.
  • 40
    • 0000499548 scopus 로고
    • PTPKAV 0033-068X 10.1143/PTP.76.1237
    • J. Hara and K. Nagai, Prog. Theor. Phys. 76, 1237 (1986). PTPKAV 0033-068X 10.1143/PTP.76.1237
    • (1986) Prog. Theor. Phys. , vol.76 , pp. 1237
    • Hara, J.1    Nagai, K.2
  • 43
    • 21844503716 scopus 로고
    • JUPSAU 0031-9015 10.1143/JPSJ.64.1703
    • M. Matsumoto and H. Shiba, J. Phys. Soc. Jpn. 64, 1703 (1995). JUPSAU 0031-9015 10.1143/JPSJ.64.1703
    • (1995) J. Phys. Soc. Jpn. , vol.64 , pp. 1703
    • Matsumoto, M.1    Shiba, H.2
  • 47
    • 70349918323 scopus 로고    scopus 로고
    • (R). PRBMDO 1098-0121 10.1103/PhysRevB.80.100506
    • T. Micklitz and M. R. Norman, Phys. Rev. B 80, 100506 (R) (2009). PRBMDO 1098-0121 10.1103/PhysRevB.80.100506
    • (2009) Phys. Rev. B , vol.80 , pp. 100506
    • Micklitz, T.1    Norman, M.R.2
  • 49
    • 84861673291 scopus 로고    scopus 로고
    • (R). PRBMDO 1098-0121 10.1103/PhysRevB.85.180509
    • A. Yamakage, K. Yada, M. Sato, and Y. Tanaka, Phys. Rev. B 85, 180509 (R) (2012). PRBMDO 1098-0121 10.1103/PhysRevB.85.180509
    • (2012) Phys. Rev. B , vol.85 , pp. 180509
    • Yamakage, A.1    Yada, K.2    Sato, M.3    Tanaka, Y.4
  • 53
    • 33947233708 scopus 로고    scopus 로고
    • JUPSAU 0031-9015 10.1143/JPSJ.76.034711
    • A. Kobayashi and S. Katayama, J. Phys. Soc. Jpn. 76, 034711 (2007). JUPSAU 0031-9015 10.1143/JPSJ.76.034711
    • (2007) J. Phys. Soc. Jpn. , vol.76 , pp. 034711
    • Kobayashi, A.1    Katayama, S.2
  • 55
    • 84884470703 scopus 로고    scopus 로고
    • PRBMDO 1098-0121 10.1103/PhysRevB.88.075142
    • 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


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.