메뉴 건너뛰기




Volumn 16, Issue 2, 2013, Pages 137-170

Topological Invariants of Edge States for Periodic Two-Dimensional Models

Author keywords

Bloch theory; Edge states; Topological invariants

Indexed keywords


EID: 84878811040     PISSN: 13850172     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11040-012-9123-9     Document Type: Article
Times cited : (114)

References (21)
  • 1
    • 0000784603 scopus 로고
    • Numerical study of symmetry effects on localization in two dimensions
    • Ando, T.: Numerical study of symmetry effects on localization in two dimensions. Phys. Rev. B40, 5325-5339 (1989).
    • (1989) Phys. Rev. , vol.B40 , pp. 5325-5339
    • Ando, T.1
  • 2
    • 0036025748 scopus 로고    scopus 로고
    • Equality of bulk and edge Hall conductance revisited
    • Elbau, P., Graf, G.-M.: Equality of bulk and edge Hall conductance revisited. Commun. Math. Phys. 229, 415-432 (2002).
    • (2002) Commun. Math. Phys. , vol.229 , pp. 415-432
    • Elbau, P.1    Graf, G.-M.2
  • 3
    • 84878813467 scopus 로고    scopus 로고
    • Quantum theory of large systems of non-relativistic matter
    • New York: Elsevier
    • Fröhlich, J., Studer, U. M., Thiran, E.: Quantum theory of large systems of non-relativistic matter. In: Les Houches Lectures 1994. Elsevier, New York (1996).
    • (1996) Les Houches Lectures 1994
    • Fröhlich, J.1    Studer, U.M.2    Thiran, E.3
  • 6
    • 23544435097 scopus 로고
    • Quantized Hall conductance, current-carrying edge states, and the existence of extended states in a two-dimensional disordered potential
    • Halperin, B. I.: Quantized Hall conductance, current-carrying edge states, and the existence of extended states in a two-dimensional disordered potential. Phys. Rev. B 25, 2185-2190 (1982).
    • (1982) Phys. Rev. B , vol.25 , pp. 2185-2190
    • Halperin, B.I.1
  • 7
    • 4243734768 scopus 로고
    • The Chern number and edge states in the integer quantum hall effect
    • Hatsugai, Y.: The Chern number and edge states in the integer quantum hall effect. Phys. Rev. Lett. 71, 3697-3700 (1993).
    • (1993) Phys. Rev. Lett. , vol.71 , pp. 3697-3700
    • Hatsugai, Y.1
  • 8
    • 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., Aoki, H.: Topological analysis of the quantum Hall effect in graphene: Dirac-Fermi transition across van Hove singularities and edge versus bulk quantum numbers. Phys. Rev. B74, 205414-205430 (2006).
    • (2006) Phys. Rev. , vol.B74 , pp. 205414-205430
    • Hatsugai, Y.1    Fukui, T.2    Aoki, H.3
  • 9
    • 28844477210 scopus 로고    scopus 로고
    • 2 topological order and the quantum spin Hall effect
    • 2 topological order and the quantum spin Hall effect. Phys. Rev. Lett. 95, 146802-145805 (2005).
    • (2005) Phys. Rev. Lett. , vol.95 , pp. 145805-146802
    • Kane, C.L.1    Mele, E.J.2
  • 10
    • 0036002351 scopus 로고    scopus 로고
    • Edge current channels and Chern numbers in the integer quantum Hall effect
    • Kellendonk, J., Richter, T., Schulz-Baldes, H.: Edge current channels and Chern numbers in the integer quantum Hall effect. Rev. Math. Phys. 14, 87-119 (2002).
    • (2002) Rev. Math. Phys. , vol.14 , pp. 87-119
    • Kellendonk, J.1    Richter, T.2    Schulz-Baldes, H.3
  • 11
    • 0003109280 scopus 로고
    • Principles of the theory of λ-zones of stability of a canonical system of linear differential equations with periodic coefficients
    • Izdat. Akad. Nauk SSSR, Moscow (1955) (English Transl.: Krein, M. G.: Topics in Differential and Integral Equations and Operator Theory. Birkhäuser, Boston
    • Krein, M. G.: Principles of the theory of λ-zones of stability of a canonical system of linear differential equations with periodic coefficients. In: Memory of A. A. Andronov, pp. 413-498. Izdat. Akad. Nauk SSSR, Moscow (1955) (English Transl.: Krein, M. G.: Topics in Differential and Integral Equations and Operator Theory. Birkhäuser, Boston (1983)).
    • (1983) Memory of A. A. Andronov , pp. 413-498
    • Krein, M.G.1
  • 12
    • 19944375123 scopus 로고    scopus 로고
    • Quantum Graphs II: some spectral properties of quantum and combinatorial graphs
    • Kuchment, P.: Quantum Graphs II: some spectral properties of quantum and combinatorial graphs. J. Phys. A38, 4887-4900 (2005).
    • (2005) J. Phys. , vol.A38 , pp. 4887-4900
    • Kuchment, P.1
  • 13
    • 0141908215 scopus 로고    scopus 로고
    • Flat bands of a tight-binding electronic system with hexagonal structure
    • Nishino, S., Goda, M., Kusakabe, K.: Flat bands of a tight-binding electronic system with hexagonal structure. J. Phys. Soc. Jpn. 72, 2015-2023 (2003).
    • (2003) J. Phys. Soc. Jpn. , vol.72 , pp. 2015-2023
    • Nishino, S.1    Goda, M.2    Kusakabe, K.3
  • 14
    • 70350736172 scopus 로고    scopus 로고
    • Robustness of the spin-Chern number
    • Prodan, E.: Robustness of the spin-Chern number. Phys. Rev. B80, 125327-125333 (2009).
    • (2009) Phys. Rev. , vol.B80 , pp. 125327-125333
    • Prodan, E.1
  • 15
    • 76349120157 scopus 로고    scopus 로고
    • Random Dirac operators with time reversal symmetry
    • Sadel, C., Schulz-Baldes, H.: Random Dirac operators with time reversal symmetry. Commun. Math. Phys. 295, 209-242 (2010).
    • (2010) Commun. Math. Phys. , vol.295 , pp. 209-242
    • Sadel, C.1    Schulz-Baldes, H.2
  • 16
    • 35548947617 scopus 로고    scopus 로고
    • Rotation numbers for Jacobi matrices with matrix entries
    • Schulz-Baldes, H.: Rotation numbers for Jacobi matrices with matrix entries. Math. Phys. Electron. J. 13, 40 pp. (2007).
    • (2007) Math. Phys. Electron. J , vol.13 , pp. 40
    • Schulz-Baldes, H.1
  • 17
    • 77951779727 scopus 로고    scopus 로고
    • Geometry of Weyl theory for Jacobi matrices with matrix entries
    • Schulz-Baldes, H.: Geometry of Weyl theory for Jacobi matrices with matrix entries. J. Anal. Math. 110, 129-165 (2010).
    • (2010) J. Anal. Math. , vol.110 , pp. 129-165
    • Schulz-Baldes, H.1
  • 18
    • 0034695295 scopus 로고    scopus 로고
    • Edge versus Bulk currents in the integer quantum hall effect
    • Schulz-Baldes, H., Kellendonk, J., Richter, T.: Edge versus Bulk currents in the integer quantum hall effect. J. Phys. A33, L27-L32 (2000).
    • (2000) J. Phys , vol.A33 , pp. 27-32
    • Schulz-Baldes, H.1    Kellendonk, J.2    Richter, T.3
  • 19
    • 33746255952 scopus 로고    scopus 로고
    • Quantum spin-hall effect and topologically invariant Chern numbers
    • Sheng, D. N., Weng, Z. Y., Sheng, L., Haldane, F. D. M.: Quantum spin-hall effect and topologically invariant Chern numbers. Phys. Rev. Lett. 97, 036808-036811 (2006).
    • (2006) Phys. Rev. Lett. , vol.97 , pp. 36808-36811
    • Sheng, D.N.1    Weng, Z.Y.2    Sheng, L.3    Haldane, F.D.M.4
  • 20
    • 34147178700 scopus 로고
    • On the surface states associated with a periodic potential
    • Shockley, W.: On the surface states associated with a periodic potential. Phys. Rev. 56, 317-323 (1939).
    • (1939) Phys. Rev. , vol.56 , pp. 317-323
    • Shockley, W.1
  • 21
    • 33646091010 scopus 로고
    • Über eine mögliche Art der Elektronenbindung an Kristalloberflächen
    • Tamm, I.: Über eine mögliche Art der Elektronenbindung an Kristalloberflächen. Z. Phys. Sov. 76, 849-850 (1932).
    • (1932) Z. Phys. Sov. , vol.76 , pp. 849-850
    • Tamm, I.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.