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Volumn 88, Issue 7, 2013, Pages

Classification of massive and gapless phases in bilayer graphene

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EID: 84884410494     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.88.075415     Document Type: Article
Times cited : (29)

References (102)
  • 2
    • 3442881546 scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.53.2449
    • G. W. Semenoff, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.53. 2449 53, 2449 (1984).
    • (1984) Phys. Rev. Lett. , vol.53 , pp. 2449
    • Semenoff, G.W.1
  • 6
    • 33644674176 scopus 로고    scopus 로고
    • Landau-level degeneracy and quantum hall effect in a graphite bilayer
    • DOI 10.1103/PhysRevLett.96.086805, 086805
    • E. McCann and V. I. Falko, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.086805 96, 086805 (2006). (Pubitemid 43334272)
    • (2006) Physical Review Letters , vol.96 , Issue.8 , pp. 1-4
    • McCann, E.1    Fal'ko, V.I.2
  • 7
    • 78649746048 scopus 로고    scopus 로고
    • EULEEJ 0295-5075 10.1209/0295-5075/87/47008
    • J. Kailasvuori, Eur. Phys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/87/ 47008 87, 47008 (2009).
    • (2009) Eur. Phys. Lett. , vol.87 , pp. 47008
    • Kailasvuori, J.1
  • 8
    • 0000987088 scopus 로고
    • 0556-2791 10.1103/PhysRevA.19.2461
    • Y. Aharonov and A. Casher, Phys. Rev. A 0556-2791 10.1103/PhysRevA.19. 2461 19, 2461 (1979);
    • (1979) Phys. Rev. A , vol.19 , pp. 2461
    • Aharonov, Y.1    Casher, A.2
  • 9
    • 0000607713 scopus 로고
    • 0556-2821 10.1103/PhysRevD.29.2375
    • R. Jackiw, Phys. Rev. D 0556-2821 10.1103/PhysRevD.29.2375 29, 2375 (1984);
    • (1984) Phys. Rev. D , vol.29 , pp. 2375
    • Jackiw, R.1
  • 10
    • 79961106369 scopus 로고    scopus 로고
    • PRBMDO 1098-0121 10.1103/PhysRevB.83.195422
    • B. Roy and I. F. Herbut, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.83.195422 83, 195422 (2011);
    • (2011) Phys. Rev. B , vol.83 , pp. 195422
    • Roy, B.1    Herbut, I.F.2
  • 12
    • 78650891702 scopus 로고    scopus 로고
    • 1943-2879 10.1103/Physics.2.57
    • I. F. Herbut, Physics 1943-2879 10.1103/Physics.2.57 2, 57 (2009).
    • (2009) Physics , vol.2 , pp. 57
    • Herbut, I.F.1
  • 13
    • 77954825946 scopus 로고    scopus 로고
    • PRBMDO 1098-0121 10.1103/PhysRevB.81.041401
    • O. Vafek and K. Yang, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.81. 041401 81, 041401 (R) (2010).
    • (2010) Phys. Rev. B , vol.81 , pp. 041401
    • Vafek, O.1    Yang, K.2
  • 14
    • 68849089683 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.103.046811
    • K. Sun, H. Yao, E. Fradkin, and S. A. Kivelson, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.103.046811 103, 046811 (2009).
    • (2009) Phys. Rev. Lett. , vol.103 , pp. 046811
    • Sun, K.1    Yao, H.2    Fradkin, E.3    Kivelson, S.A.4
  • 15
    • 84884401778 scopus 로고    scopus 로고
    • If we neglect the trigonal warping, which otherwise breaks the quadratic band touching near each valley into four Dirac cones, intrinsic screening (Thomas-Fermi screening) due to the finite density of states at Fermi energy turns the interactions into short-ranged ones. However, the vanishing density of state at the Fermi energy due to the trigonal warping restores the long-range nature of the Coulomb interaction.
    • If we neglect the trigonal warping, which otherwise breaks the quadratic band touching near each valley into four Dirac cones, intrinsic screening (Thomas-Fermi screening) due to the finite density of states at Fermi energy turns the interactions into short-ranged ones. However, the vanishing density of state at the Fermi energy due to the trigonal warping restores the long-range nature of the Coulomb interaction.
  • 16
    • 84867026293 scopus 로고    scopus 로고
    • PRBMDO 1098-0121 10.1103/PhysRevB.86.115447
    • R. E. Throckmorton and O. Vafek, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.86.115447 86, 115447 (2012).
    • (2012) Phys. Rev. B , vol.86 , pp. 115447
    • Throckmorton, R.E.1    Vafek, O.2
  • 23
    • 77954827092 scopus 로고    scopus 로고
    • PRBMDO 1098-0121 10.1103/PhysRevB.81.041402
    • F. Zhang, H. Min, M. Polini, and A. H. MacDonald, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.81.041402 81, 041402 (2010).
    • (2010) Phys. Rev. B , vol.81 , pp. 041402
    • Zhang, F.1    Min, H.2    Polini, M.3    Macdonald, A.H.4
  • 24
    • 77951028564 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.104.156803
    • R. Nandkishore and L. Levitov, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.104.156803 104, 156803 (2010).
    • (2010) Phys. Rev. Lett. , vol.104 , pp. 156803
    • Nandkishore, R.1    Levitov, L.2
  • 27
    • 33747876356 scopus 로고
    • PHRVAO 0031-899X 10.1103/PhysRev.135.A550
    • P. Fulde and R. A. Ferrell, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.135.A550 135, A550 (1964).
    • (1964) Phys. Rev. , vol.135 , pp. 550
    • Fulde, P.1    Ferrell, R.A.2
  • 28
    • 84857408654 scopus 로고    scopus 로고
    • PHSTBO 0031-8949 10.1088/0031-8949/2012/T146/014011
    • R. Nandkishore and L. Levitov, Phys. Scr. T PHSTBO 0031-8949 10.1088/0031-8949/2012/T146/014011 146, 014011 (2012).
    • (2012) Phys. Scr. T , vol.146 , pp. 014011
    • Nandkishore, R.1    Levitov, L.2
  • 29
    • 2542483412 scopus 로고    scopus 로고
    • EPJBFY 1434-6028 10.1140/epjb/e2004-00092-2
    • T. A. Gloor and F. Milla, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2004-00092-2 38, 9 (2004).
    • (2004) Eur. Phys. J. B , vol.38 , pp. 9
    • Gloor, T.A.1    Milla, F.2
  • 32
    • 77955164970 scopus 로고    scopus 로고
    • PRBMDO 1098-0121 10.1103/PhysRevB.81.125435
    • R. van Gelderen and C. M. Smith, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.81.125435 81, 125435 (2010).
    • (2010) Phys. Rev. B , vol.81 , pp. 125435
    • Van Gelderen, R.1    Smith, C.M.2
  • 33
    • 78649732372 scopus 로고    scopus 로고
    • PRBMDO 1098-0121 10.1103/PhysRevB.82.205106
    • O. Vafek, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.82.205106 82, 205106 (2010).
    • (2010) Phys. Rev. B , vol.82 , pp. 205106
    • Vafek, O.1
  • 34
    • 33749324120 scopus 로고    scopus 로고
    • Interactions and phase transitions on Graphene's honeycomb lattice
    • DOI 10.1103/PhysRevLett.97.146401
    • I. F. Herbut, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97. 146401 97, 146401 (2006); (Pubitemid 44498323)
    • (2006) Physical Review Letters , vol.97 , Issue.14 , pp. 146401
    • Herbut, I.F.1
  • 36
    • 67449108457 scopus 로고    scopus 로고
    • PRBMDO 1098-0121 10.1103/PhysRevB.79.184520
    • D. L. Bergman and K. Le Hur, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.79.184520 79, 184520 (2009).
    • (2009) Phys. Rev. B , vol.79 , pp. 184520
    • Bergman, D.L.1    Le Hur, K.2
  • 37
    • 67449098417 scopus 로고    scopus 로고
    • PRBMDO 1098-0121 10.1103/PhysRevB.79.193405
    • I. F. Herbut, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.79.193405 79, 193405 (2009).
    • (2009) Phys. Rev. B , vol.79 , pp. 193405
    • Herbut, I.F.1
  • 38
    • 0036752394 scopus 로고    scopus 로고
    • PRBMDO 0163-1829 10.1103/PhysRevB.66.094504
    • I. F. Herbut, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.66.094504 66, 094504 (2002);
    • (2002) Phys. Rev. B , vol.66 , pp. 094504
    • Herbut, I.F.1
  • 39
    • 27744451308 scopus 로고    scopus 로고
    • Effective theory of high-temperature superconductors
    • DOI 10.1103/PhysRevLett.94.237001, 237001
    • I. F. Herbut, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94. 237001 94, 237001 (2005); (Pubitemid 41636571)
    • (2005) Physical Review Letters , vol.94 , Issue.23 , pp. 1-4
    • Herbut, I.F.1
  • 40
    • 0036751907 scopus 로고    scopus 로고
    • PRBMDO 0163-1829 10.1103/PhysRevB.66.094512
    • D. J. Lee and I. F. Herbut, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.66.094512 66, 094512 (2002);
    • (2002) Phys. Rev. B , vol.66 , pp. 094512
    • Lee, D.J.1    Herbut, I.F.2
  • 41
    • 0141536945 scopus 로고    scopus 로고
    • PRBMDO 0163-1829 10.1103/PhysRevB.65.180511
    • Z. Tešanović, O. Vafek, and M. Franz, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.65.180511 65, 180511 (2002);
    • (2002) Phys. Rev. B , vol.65 , pp. 180511
    • Tešanović, Z.1    Vafek, O.2    Franz, M.3
  • 43
    • 34247527303 scopus 로고    scopus 로고
    • PRBMDO 1098-0121 10.1103/PhysRevB.75.134516
    • I. O. Thomas and S. Hands, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.75.134516 75, 134516 (2007).
    • (2007) Phys. Rev. B , vol.75 , pp. 134516
    • Thomas, I.O.1    Hands, S.2
  • 46
    • 36148991143 scopus 로고    scopus 로고
    • PRBMDO 1098-0121 10.1103/PhysRevB.76.195415
    • I. L. Aleiner, D. E. Kharzeev, and A. M. Tsvelik, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.76.195415 76, 195415 (2007).
    • (2007) Phys. Rev. B , vol.76 , pp. 195415
    • Aleiner, I.L.1    Kharzeev, D.E.2    Tsvelik, A.M.3
  • 47
    • 38749108463 scopus 로고    scopus 로고
    • Coulomb interaction, ripples, and the minimal conductivity of graphene
    • DOI 10.1103/PhysRevLett.100.046403
    • I. F. Herbut, V. Juričić, and O. Vafek, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.046403 100, 046403 (2008). (Pubitemid 351185681)
    • (2008) Physical Review Letters , vol.100 , Issue.4 , pp. 046403
    • Herbut, I.F.1    Juricic, V.2    Vafek, O.3
  • 50
    • 0000783193 scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.61.2015
    • F. D. M. Haldane, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 61.2015 61, 2015 (1988).
    • (1988) Phys. Rev. Lett. , vol.61 , pp. 2015
    • Haldane, F.D.M.1
  • 51
    • 84863001164 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.108.266402
    • C.-K. Lu and I. F. Herbut, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.108.266402 108, 266402 (2012).
    • (2012) Phys. Rev. Lett. , vol.108 , pp. 266402
    • Lu, C.-K.1    Herbut, I.F.2
  • 52
    • 34247877557 scopus 로고    scopus 로고
    • Electron fractionalization in two-dimensional graphenelike structures
    • DOI 10.1103/PhysRevLett.98.186809
    • C.-Y. Hou, C. Chamon, and C. Mudry, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.186809 98, 186809 (2007). (Pubitemid 46701718)
    • (2007) Physical Review Letters , vol.98 , Issue.18 , pp. 186809
    • Hou, C.-Y.1    Chamon, C.2    Mudry, C.3
  • 53
    • 84884408272 scopus 로고    scopus 로고
    • The Cl(3) group is a set of three mutually anticommuting matrices. See for example Ref..
    • The Cl (3) group is a set of three mutually anticommuting matrices. See for example Ref..
  • 56
    • 34249864462 scopus 로고    scopus 로고
    • Spontaneous symmetry breaking and quantum Hall effect in graphene
    • DOI 10.1016/j.ssc.2007.03.051, PII S0038109807003006, Exploring graphene Recent research advances
    • See also K. Yang, Solid State Commun. SSCOA4 0038-1098 10.1016/j.ssc.2007.03.051 143, 27 (2007); (Pubitemid 46874500)
    • (2007) Solid State Communications , vol.143 , Issue.1-2 , pp. 27-32
    • Yang, K.1
  • 57
    • 84855762487 scopus 로고    scopus 로고
    • NNOTER 0957-4484 10.1088/0957-4484/23/5/052001
    • Y. Barlas, Kun Yang, and A. H. MacDonald, Nanotechnology NNOTER 0957-4484 10.1088/0957-4484/23/5/052001 23, 052001 (2012).
    • (2012) Nanotechnology , vol.23 , pp. 052001
    • Barlas, Y.1    Yang, K.2    Macdonald, A.H.3
  • 58
    • 28844482338 scopus 로고    scopus 로고
    • Unconventional integer quantum hall effect in graphene
    • DOI 10.1103/PhysRevLett.95.146801, 146801
    • V. P. Gusynin and S. G. Sharapov, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.146801 95, 146801 (2005); (Pubitemid 41777601)
    • (2005) Physical Review Letters , vol.95 , Issue.14 , pp. 1-4
    • Gusynin, V.P.1    Sharapov, S.G.2
  • 60
    • 34247394616 scopus 로고    scopus 로고
    • PRBMDO 1098-0121 10.1103/PhysRevB.75.165411
    • I. F. Herbut, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.75.165411 75, 165411 (2007);
    • (2007) Phys. Rev. B , vol.75 , pp. 165411
    • Herbut, I.F.1
  • 61
    • 34548288589 scopus 로고    scopus 로고
    • PRBMDO 1098-0121 10.1103/PhysRevB.76.085432
    • I. F. Herbut, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.76.085432 76, 085432 (2007);
    • (2007) Phys. Rev. B , vol.76 , pp. 085432
    • Herbut, I.F.1
  • 62
    • 46049095556 scopus 로고    scopus 로고
    • PRBMDO 1098-0121 10.1103/PhysRevB.77.245438
    • I. F. Herbut and B. Roy, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.77.245438 77, 245438 (2008);
    • (2008) Phys. Rev. B , vol.77 , pp. 245438
    • Herbut, I.F.1    Roy, B.2
  • 64
    • 77957701366 scopus 로고    scopus 로고
    • PRBMDO 1098-0121 10.1103/PhysRevB.82.115124
    • R. Nandkishore and L. Levitov, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.82.115124 82, 115124 (2010).
    • (2010) Phys. Rev. B , vol.82 , pp. 115124
    • Nandkishore, R.1    Levitov, L.2
  • 65
    • 77955361784 scopus 로고    scopus 로고
    • PRBMDO 1098-0121 10.1103/PhysRevB.81.155451
    • E. V. Gorbar, V. P. Gusynin, and V. A. Miransky, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.81.155451 81, 155451 (2010);
    • (2010) Phys. Rev. B , vol.81 , pp. 155451
    • Gorbar, E.V.1    Gusynin, V.P.2    Miransky, V.A.3
  • 68
    • 84870409107 scopus 로고    scopus 로고
    • PRBMDO 1098-0121 10.1103/PhysRevB.86.195435
    • M. Kharitonov, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.86.195435 86, 195435 (2012);
    • (2012) Phys. Rev. B , vol.86 , pp. 195435
    • Kharitonov, M.1
  • 71
    • 84871598281 scopus 로고    scopus 로고
    • PRBMDO 1098-0121 10.1103/PhysRevB.86.235126
    • X.-Z. Yan and C. S. Ting, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.86.235126 86, 235126 (2012);
    • (2012) Phys. Rev. B , vol.86 , pp. 235126
    • Yan, X.-Z.1    Ting, C.S.2
  • 72
    • 84873019062 scopus 로고    scopus 로고
    • 10.1103/PhysRevB.87.035427
    • L. Zhu, V. Aji, and C. M. Varma, Phys. Rev. B 10.1103/PhysRevB.87.035427 87, 035427 (2013).
    • (2013) Phys. Rev. B , vol.87 , pp. 035427
    • Zhu, L.1    Aji, V.2    Varma, C.M.3
  • 73
    • 84884386782 scopus 로고    scopus 로고
    • arXiv: 1203.6340.
    • B. Roy, arXiv: 1203.6340.
    • Roy, B.1
  • 74
    • 77956708648 scopus 로고    scopus 로고
    • PRBMDO 1098-0121 10.1103/PhysRevB.82.035429
    • B. Roy and I. F. Herbut, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.82.035429 82, 035429 (2010).
    • (2010) Phys. Rev. B , vol.82 , pp. 035429
    • Roy, B.1    Herbut, I.F.2
  • 75
    • 77950853233 scopus 로고    scopus 로고
    • PRBMDO 1098-0121 10.1103/PhysRevB.80.205319
    • S. Ryu, C. Mudry, C.-Y. Hou, and C. Chamon, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.80.205319 80, 205319 (2009).
    • (2009) Phys. Rev. B , vol.80 , pp. 205319
    • Ryu, S.1    Mudry, C.2    Hou, C.-Y.3    Chamon, C.4
  • 76
    • 33845351809 scopus 로고    scopus 로고
    • BCS-BEC crossover on the two-dimensional honeycomb lattice
    • DOI 10.1103/PhysRevLett.97.230404
    • E. Zhao and A. Paramekanti, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.230404 97, 230404 (2006). (Pubitemid 44888136)
    • (2006) Physical Review Letters , vol.97 , Issue.23 , pp. 230404
    • Zhao, E.1    Paramekanti, A.2
  • 77
    • 42149173872 scopus 로고    scopus 로고
    • Density waves and cooper pairing on the honeycomb lattice
    • DOI 10.1103/PhysRevLett.100.146404
    • C. Honerkamp, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100. 146404 100, 146404 (2008). (Pubitemid 351535529)
    • (2008) Physical Review Letters , vol.100 , Issue.14 , pp. 146404
    • Honerkamp, C.1
  • 81
    • 42249099225 scopus 로고    scopus 로고
    • Topological mott insulators
    • DOI 10.1103/PhysRevLett.100.156401
    • S. Raghu, X.-Liang Qi, C. Honerkamp, and S.-C. Zhang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.156401 100, 156401 (2008). (Pubitemid 351549477)
    • (2008) Physical Review Letters , vol.100 , Issue.15 , pp. 156401
    • Raghu, S.1    Qi, X.-L.2    Honerkamp, C.3    Zhang, S.-C.4
  • 82
    • 84881127962 scopus 로고    scopus 로고
    • PRBMDO 1098-0121 10.1103/PhysRevB.88.045425
    • B. Roy and I. F. Herbut, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.88.045425 88, 045425 (2013).
    • (2013) Phys. Rev. B , vol.88 , pp. 045425
    • Roy, B.1    Herbut, I.F.2
  • 83
    • 84865646997 scopus 로고    scopus 로고
    • PRBMDO 1098-0121 10.1103/PhysRevB.86.075467
    • V. Cvetkovic, R. E. Throckmorton, and O. Vafek, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.86.075467 86, 075467 (2012).
    • (2012) Phys. Rev. B , vol.86 , pp. 075467
    • Cvetkovic, V.1    Throckmorton, R.E.2    Vafek, O.3
  • 84
    • 84863336471 scopus 로고    scopus 로고
    • PRBMDO 1098-0121 10.1103/PhysRevB.85.245451
    • Y. Lemonik, I. L. Aleiner, and V. I. Fal'ko, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.85.245451 85, 245451 (2012).
    • (2012) Phys. Rev. B , vol.85 , pp. 245451
    • Lemonik, Y.1    Aleiner, I.L.2    Fal'Ko, V.I.3
  • 85
    • 77950842509 scopus 로고    scopus 로고
    • For Monte Carlo simulation of Hubbard-U. model in monolayer graphene, see, NATUAS 0028-0836 10.1038/nature08942
    • For Monte Carlo simulation of Hubbard-U. model in monolayer graphene, see Z. Y. Meng, T. C. Lang, S. Wessel, F. F. Assaad, and A. Muramatsu, Nature (London) NATUAS 0028-0836 10.1038/nature08942 464, 847 (2010);
    • (2010) Nature (London) , vol.464 , pp. 847
    • Meng, Z.Y.1    Lang, T.C.2    Wessel, S.3    Assaad, F.F.4    Muramatsu, A.5
  • 90
    • 28844477796 scopus 로고    scopus 로고
    • Quantum Spin hall effect in graphene
    • DOI 10.1103/PhysRevLett.95.226801, 226801
    • C. L. Kane and E. J. Mele, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.226801 95, 226801 (2005). (Pubitemid 41776999)
    • (2005) Physical Review Letters , vol.95 , Issue.22 , pp. 1-4
    • Kane, C.L.1    Mele, E.J.2
  • 94
    • 70349139662 scopus 로고    scopus 로고
    • For quantum phase transitions in monolayer graphene, see, PRBMDO 1098-0121 10.1103/PhysRevB.80.075432
    • For quantum phase transitions in monolayer graphene, see I. F. Herbut, V. Juričić, and O. Vafek, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.80.075432 80, 075432 (2009);
    • (2009) Phys. Rev. B , vol.80 , pp. 075432
    • Herbut, I.F.1    Juričić, V.2    Vafek, O.3
  • 95
    • 70349462529 scopus 로고    scopus 로고
    • PRBMDO 1098-0121 10.1103/PhysRevB.80.081405
    • V. Juričić, I. F. Herbut, and G. W. Semenoff, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.80.081405 80, 081405 (R) (2009);
    • (2009) Phys. Rev. B , vol.80 , pp. 081405
    • Juričić, V.1    Herbut, I.F.2    Semenoff, G.W.3
  • 96
    • 80053590237 scopus 로고    scopus 로고
    • PRBMDO 1098-0121 10.1103/PhysRevB.84.113404
    • B. Roy, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.84.113404 84, 113404 (2011);
    • (2011) Phys. Rev. B , vol.84 , pp. 113404
    • Roy, B.1
  • 97
    • 84872235705 scopus 로고    scopus 로고
    • PRBMDO 1098-0121 10.1103/PhysRevB.87.041401
    • B. Roy, V. Juričić, and I. F. Herbut, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.87.041401 87, 041401 (R) (2013).
    • (2013) Phys. Rev. B , vol.87 , pp. 041401
    • Roy, B.1    Juričić, V.2    Herbut, I.F.3
  • 98
    • 84857759196 scopus 로고    scopus 로고
    • PRBMDO 1098-0121 10.1103/PhysRevB.85.085304
    • I. F. Herbut, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.85.085304 85, 085304 (2012).
    • (2012) Phys. Rev. B , vol.85 , pp. 085304
    • Herbut, I.F.1
  • 99
    • 84884407891 scopus 로고    scopus 로고
    • For example, one can take Ψ≡Φ, as in Eqs. and , yielding such a particular form of the kinetic-energy term.
    • For example, one can take Ψ ≡ Φ, as in Eqs. and, yielding such a particular form of the kinetic-energy term.
  • 100
    • 0000023684 scopus 로고    scopus 로고
    • PRBMDO 0163-1829 10.1103/PhysRevB.55.1142
    • A. Altland and M. R. Zirnbauer, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.55.1142 55, 1142 (1997).
    • (1997) Phys. Rev. B , vol.55 , pp. 1142
    • Altland, A.1    Zirnbauer, M.R.2
  • 101
    • 0000306769 scopus 로고
    • JMAPAQ 0022-2488 10.1063/1.529277
    • S. Okubo, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.529277 32, 1657 (1991).
    • (1991) J. Math. Phys. , vol.32 , pp. 1657
    • Okubo, S.1
  • 102
    • 84884369029 scopus 로고    scopus 로고
    • See also Table 1 in Ref..
    • See also Table 1 in Ref..


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