메뉴 건너뛰기




Volumn , Issue 18, 2014, Pages

A study of the ambiguity in the solutions to the Diophantine equation for Chern numbers

Author keywords

Diophantine equations; Hofstadter model; quantum Hall phase diagrams; window conditions

Indexed keywords


EID: 84905733906     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/47/18/185202     Document Type: Article
Times cited : (23)

References (19)
  • 1
    • 0041969649 scopus 로고    scopus 로고
    • A topological look at the quantum Hall effect
    • Avron J E, Osadchy D and Seiler R 2003 A topological look at the quantum Hall effect Phys. Today 56 38-42
    • (2003) Phys. Today , vol.56 , pp. 38-42
    • Avron, J.E.1    Osadchy, D.2    Seiler, R.3
  • 2
    • 36149029662 scopus 로고
    • Analysis of the spectrum of a particle on a triangular lattice with two magnetic fluxes by algebraic and numerical methods
    • Bellissard J, Kreft C and Seiler R 1991 Analysis of the spectrum of a particle on a triangular lattice with two magnetic fluxes by algebraic and numerical methods J. Phys. A: Math. Gen. 24 2329
    • (1991) J. Phys. A: Math. Gen. , vol.24 , Issue.10 , pp. 2329
    • Bellissard, J.1    Kreft, C.2    Seiler, R.3
  • 3
    • 0000407064 scopus 로고
    • Cantor spectrum for the almost Mathieu equation
    • Bellissard J and Simon B 1982 Cantor spectrum for the almost Mathieu equation J. Funct. Anal. 48 408-19
    • (1982) J. Funct. Anal. , vol.48 , pp. 408-419
    • Bellissard, J.1    Simon, B.2
  • 5
    • 0002207807 scopus 로고
    • Quantal phase factors accompanying adiabatic changes
    • Berry M V 1984 Quantal phase factors accompanying adiabatic changes Proc. R. Soc. A 392 45-57
    • (1984) Proc. R. Soc. , vol.392 , pp. 45-57
    • Berry, M.V.1
  • 6
    • 0000194760 scopus 로고
    • Linear-network model for magnetic breakdown in two dimensions
    • Chambers W G 1965 Linear-network model for magnetic breakdown in two dimensions Phys. Rev. 140 A135-43
    • (1965) Phys. Rev. , vol.140 , pp. 135-A143
    • Chambers, W.G.1
  • 7
  • 8
    • 0001062004 scopus 로고
    • Magnetic subband structure of electrons in hexagonal lattices
    • Claro F H and Wannier G H 1979 Magnetic subband structure of electrons in hexagonal lattices Phys. Rev. B 19 6068-74
    • (1979) Phys. Rev. , vol.19 , pp. 6068-6074
    • Claro, F.H.1    Wannier, G.H.2
  • 9
  • 11
    • 84944867777 scopus 로고    scopus 로고
    • Agazzi A, Eckmann J-P and Graf G M 2014 The colored Hofstadter butterfly for the honeycomb lattice (http://xxx.lanl.gov/abs/1403.1270v1)
    • (2014)
    • Agazzi, A.1    Eckmann, J.-P.2    Graf, G.M.3
  • 12
    • 0000631349 scopus 로고
    • Critical and bicritical properties of Harper's equation with next-nearest-neighbor coupling
    • Han J H, Thouless D J, Hiramoto H and Kohmoto M 1994 Critical and bicritical properties of Harper's equation with next-nearest-neighbor coupling Phys. Rev. B 50 11365-80
    • (1994) Phys. Rev. , vol.50 , pp. 11365-11380
    • Han, J.H.1    Thouless, D.J.2    Hiramoto, H.3    Kohmoto, M.4
  • 13
    • 0001615308 scopus 로고
    • Energy spectrum and the quantum Hall effect on the square lattice with next-nearest-neighbor hopping
    • Hatsugai Y and Kohmoto M 1990 Energy spectrum and the quantum Hall effect on the square lattice with next-nearest-neighbor hopping Phys. Rev. B 42 8282-94
    • (1990) Phys. Rev. , vol.42 , pp. 8282-8294
    • Hatsugai, Y.1    Kohmoto, M.2
  • 14
    • 33751011330 scopus 로고    scopus 로고
    • Topological analysis of the quantum Hall effect in graphene: Dirac-Fermi transition across van Hove singularities and edge versus bulk quantum numbers
    • Hatsugai Y, Fukui T and Aoki H 2006 Topological analysis of the quantum Hall effect in graphene: Dirac-Fermi transition across van Hove singularities and edge versus bulk quantum numbers Phys. Rev. B 74 205414
    • (2006) Phys. Rev. , vol.74
    • Hatsugai, Y.1    Fukui, T.2    Aoki, H.3
  • 15
    • 0000321758 scopus 로고
    • On the adiabatic theorem of quantum mechanics
    • Kato T 1950 On the adiabatic theorem of quantum mechanics J. Phys. Soc. Japan 5 435-9
    • (1950) J. Phys. Soc. Japan , vol.5 , pp. 435-439
    • Kato, T.1
  • 16
    • 0002660412 scopus 로고
    • The coexistence problem for the discrete Mathieu operator
    • Mouche P v 1989 The coexistence problem for the discrete Mathieu operator Commun. Math. Phys. 122 23-33
    • (1989) Commun. Math. Phys. , vol.122 , pp. 23-33
    • Mouche, P.V.1
  • 17
    • 36149041879 scopus 로고
    • Theory of quantised Hall conductivity in two dimensions
    • Streda P 1982 Theory of quantised Hall conductivity in two dimensions J. Phys. C: Solid State Phys. 15 L717
    • (1982) J. Phys. C: Solid State Phys. , vol.15 , Issue.22 , pp. 717
    • Streda, P.1
  • 19
    • 36149005273 scopus 로고
    • Magnetic translation group
    • Zak J 1964 Magnetic translation group Phys. Rev. 134 1602-6
    • (1964) Phys. Rev. , vol.134 , pp. 1602-1606
    • Zak, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.