메뉴 건너뛰기




Volumn 3, Issue 2, 2013, Pages

Protected Edge Modes without Symmetry

Author keywords

Condensed matter physics; Strongly correlated materials; Topological insulators

Indexed keywords

CONFORMAL FIELD THEORIES; ELECTRON SYSTEMS; FRACTIONAL STATISTICS; HALL CONDUCTANCE; MICROSCOPIC ANALYSIS; STRONGLY CORRELATED MATERIALS; TOPOLOGICAL INSULATORS; TWO-DIMENSIONAL ELECTRON SYSTEM;

EID: 84883159739     PISSN: None     EISSN: 21603308     Source Type: Journal    
DOI: 10.1103/PhysRevX.3.021009     Document Type: Article
Times cited : (367)

References (36)
  • 1
    • 1542763507 scopus 로고
    • Topological Orders and Edge Excitations in FQH States
    • Xiao-Gang Wen, Topological Orders and Edge Excitations in FQH States, Adv. Phys. 44, 405 (1995).
    • (1995) Adv. Phys. , vol.44 , pp. 405
    • Wen, X.-G.1
  • 3
    • 28844477796 scopus 로고    scopus 로고
    • Quantum Spin Hall Effect in Graphene
    • C. L. Kane and E. J. Mele, Quantum Spin Hall Effect in Graphene, Phys. Rev. Lett. 95, 226801 (2005).
    • (2005) Phys. Rev. Lett. , vol.95 , pp. 226801
    • Kane, C.L.1    Mele, E.J.2
  • 4
    • 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 (2005).
    • (2005) Phys. Rev. Lett. , vol.95 , pp. 146802
    • Kane, C.L.1    Mele, E.J.2
  • 5
    • 78349239882 scopus 로고    scopus 로고
    • Topological Insulators
    • M. Z. Hasan and C. L. Kane, Topological Insulators, Rev. Mod. Phys. 82, 3045 (2010).
    • (2010) Rev. Mod. Phys. , vol.82 , pp. 3045
    • Hasan, M.Z.1    Kane, C.L.2
  • 6
    • 57249110726 scopus 로고    scopus 로고
    • Classification of Topological Insulators and Superconductors in Three Spatial Dimensions
    • Andreas P. Schnyder, Shinsei Ryu, Akira Furusaki, and Andreas W.W. Ludwig, Classification of Topological Insulators and Superconductors in Three Spatial Dimensions, Phys. Rev. B 78, 195125 (2008).
    • (2008) Phys. Rev. B , vol.78 , pp. 195125
    • Schnyder, A.P.1    Ryu, S.2    Furusaki, A.3    Ludwig, A.W.W.4
  • 7
    • 0001706046 scopus 로고    scopus 로고
    • Quantized Thermal Transport in the Fractional Quantum Hall Effect
    • C. L. Kane and Matthew P.A. Fisher, Quantized Thermal Transport in the Fractional Quantum Hall Effect, Phys. Rev. B 55, 15832 (1997).
    • (1997) Phys. Rev. B , vol.55 , pp. 15832
    • Kane, C.L.1    Fisher, M.P.A.2
  • 8
    • 30444456387 scopus 로고    scopus 로고
    • Anyons in an Exactly Solved Model and Beyond
    • Alexei Kitaev, Anyons in an Exactly Solved Model and Beyond, Ann. Phys. 321, 2 (2006).
    • (2006) Ann. Phys. , vol.321 , pp. 2
    • Kitaev, A.1
  • 9
    • 0000840903 scopus 로고
    • Quantized Hall Conductivity in Two Dimensions
    • R. B. Laughlin, Quantized Hall Conductivity in Two Dimensions, Phys. Rev. B 23, 5632 (1981).
    • (1981) Phys. Rev. B , vol.23 , pp. 5632
    • Laughlin, R.B.1
  • 10
    • 23544435097 scopus 로고
    • Quantized Hall Conductance, Current-Carrying Edge States, and the Existence of Extended States in a Two-Dimensional Disordered Potential
    • Bertrand I. Halperin, Quantized Hall Conductance, Current-Carrying Edge States, and the Existence of Extended States in a Two-Dimensional Disordered Potential, Phys. Rev. B 25, 2185 (1982).
    • (1982) Phys. Rev. B , vol.25 , pp. 2185
    • Halperin, B.I.1
  • 11
    • 65649108305 scopus 로고    scopus 로고
    • Periodic Table for Topological Insulators and Superconductors
    • A.Yu. Kitaev, Periodic Table for Topological Insulators and Superconductors, AIP Conf. Proc. 1134, 22 (2009).
    • (2009) AIP Conf. Proc. , vol.1134 , pp. 22
    • Kitaev, A.Y.1
  • 12
    • 39049088106 scopus 로고    scopus 로고
    • Quantum Codes on a Lattice with Boundary
    • S. B. Bravyi and A.Y. Kitaev, Quantum Codes on a Lattice with Boundary, arXiv:quant-ph/9811052.
    • Bravyi, S.B.1    Kitaev, A.Y.2
  • 13
    • 78651428675 scopus 로고    scopus 로고
    • Topological Boundary Conditions in Abelian Chern-Simons Theory
    • Anton Kapustin and Natalia Saulina, Topological Boundary Conditions in Abelian Chern-Simons Theory, Nucl. Phys. B 845, 393 (2011).
    • (2011) Nucl. Phys. B , vol.845 , pp. 393
    • Kapustin, A.1    Saulina, N.2
  • 14
    • 84862844227 scopus 로고    scopus 로고
    • Models for Gapped Boundaries and Domain Walls
    • Alexei Kitaev and Liang Kong, Models for Gapped Boundaries and Domain Walls, Commun. Math. Phys. 313, 351 (2012).
    • (2012) Commun. Math. Phys. , vol.313 , pp. 351
    • Kitaev, A.1    Kong, L.2
  • 15
    • 70449083454 scopus 로고    scopus 로고
    • Fractional Topological Insulators
    • Michael Levin and Ady Stern, Fractional Topological Insulators, Phys. Rev. Lett. 103, 196803 (2009).
    • (2009) Phys. Rev. Lett , vol.103 , pp. 196803
    • Levin, M.1    Stern, A.2
  • 16
    • 84867031920 scopus 로고    scopus 로고
    • Classification and Analysis of Two Dimensional Abelian Fractional Topological Insulators
    • Michael Levin and Ady Stern, Classification and Analysis of Two Dimensional Abelian Fractional Topological Insulators, Phys. Rev. B 86, 115131 (2012).
    • (2012) Phys. Rev. B , vol.86 , pp. 115131
    • Levin, M.1    Stern, A.2
  • 17
    • 80455124098 scopus 로고    scopus 로고
    • Claudio Chamon, and Christopher Mudry, Fractional Topological Liquids with Time-Reversal Symmetry and Their Lattice Realization
    • Titus Neupert, Luiz Santos, Shinsei Ryu, Claudio Chamon, and Christopher Mudry, Fractional Topological Liquids with Time-Reversal Symmetry and Their Lattice Realization, Phys. Rev. B 84, 165107 (2011).
    • (2011) Phys. Rev. B , vol.84 , pp. 165107
    • Neupert, T.1    Santos, L.2    Ryu, S.3
  • 19
    • 84866382683 scopus 로고    scopus 로고
    • Theory and Classification of Interacting "Integer"Topological Phases in Two Dimensions: A Chern-Simons Approach
    • Yuan-Ming Lu and Ashvin Vishwanath, Theory and Classification of Interacting "Integer"Topological Phases in Two Dimensions: A Chern-Simons Approach, Phys. Rev. B 86, 125119 (2012).
    • (2012) Phys. Rev. B , vol.86 , pp. 125119
    • Lu, Y.-M.1    Vishwanath, A.2
  • 20
    • 84883493360 scopus 로고    scopus 로고
    • Boundary Degeneracy of Topological Order
    • Juven Wang and Xiao-Gang Wen, Boundary Degeneracy of Topological Order, arXiv:1212.4863.
    • Wang, J.1    Wen, X.-G.2
  • 21
    • 0001146528 scopus 로고
    • Stability of Chiral Luttinger Liquids and Abelian Quantum Hall States
    • F. D. M. Haldane, Stability of Chiral Luttinger Liquids and Abelian Quantum Hall States, Phys. Rev. Lett. 74, 2090 (1995).
    • (1995) Phys. Rev. Lett. , vol.74
    • Haldane, F.D.M.1
  • 22
    • 84883510487 scopus 로고    scopus 로고
    • Note that it is not important whether U(?) is relevant or irrelevant in the renormalization group sense. The reason is that we are not interested in the perturbative stability of the edge, but rather whether it is stable to arbitrary local interactions
    • Note that it is not important whether U(?) is relevant or irrelevant in the renormalization group sense. The reason is that we are not interested in the perturbative stability of the edge, but rather whether it is stable to arbitrary local interactions.
  • 23
    • 5244278223 scopus 로고
    • Classification of Abelian Quantum Hall States and Matrix Formulation of Topological Fluids
    • X. G. Wen and A. Zee, Classification of Abelian Quantum Hall States and Matrix Formulation of Topological Fluids, Phys. Rev. B 46, 2290 (1992).
    • (1992) Phys. Rev. B , vol.46 , pp. 2290
    • Wen, X.G.1    Zee, A.2
  • 24
    • 84883519259 scopus 로고    scopus 로고
    • It can be shown that the signature of K is equal to the difference between the number of left- and right-moving edge modes, nL-nR, using the bulk-edge correspondence described below
    • R, using the bulk-edge correspondence described below
  • 25
    • 84866355638 scopus 로고    scopus 로고
    • Braiding Statistics Approach to Symmetry-Protected Topological Phases
    • Michael Levin and Zheng-Cheng Gu, Braiding Statistics Approach to Symmetry-Protected Topological Phases, Phys. Rev. B 86, 115109 (2012).
    • (2012) Phys. Rev. B , vol.86 , pp. 115109
    • Levin, M.1    Gu, Z.-C.2
  • 26
    • 0043030013 scopus 로고    scopus 로고
    • Fermions, Strings, and Gauge Fields in Lattice Spin Models
    • Michael Levin and Xiao-Gang Wen, Fermions, Strings, and Gauge Fields in Lattice Spin Models, Phys. Rev. B 67, 245316 (2003).
    • (2003) Phys. Rev. B , vol.67 , pp. 245316
    • Levin, M.1    Wen, X.-G.2
  • 27
    • 33745315996 scopus 로고    scopus 로고
    • Spectral Gap and Exponential Decay of Correlations
    • Matthew B. Hastings and Tohru Koma, Spectral Gap and Exponential Decay of Correlations, Commun. Math. Phys. 265, 781 (2006).
    • (2006) Commun. Math. Phys , vol.265 , pp. 781
    • Hastings, M.B.1    Koma, T.2
  • 28
    • 0000392797 scopus 로고
    • A Proof of the Nielsen-Ninomiya Theorem
    • D. Friedan, A Proof of the Nielsen-Ninomiya Theorem, Commun. Math. Phys. 85, 481 (1982). Zemba, Modular Invariant Partition Functions in the Quantum Hall Effect, Nucl. Phys. B 490, 595 (1997).
    • (1982) Commun. Math. Phys , vol.85 , pp. 481
    • Friedan, D.1
  • 30
    • 84863329966 scopus 로고    scopus 로고
    • Interacting Topological Phases and Modular Invariance
    • Shinsei Ryu and Shou-Cheng Zhang, Interacting Topological Phases and Modular Invariance, Phys. Rev. B 85, 245132 (2012).
    • (2012) Phys. Rev. B , vol.85 , pp. 245132
    • Ryu, S.1    Zhang, S.-C.2
  • 31
    • 0031582180 scopus 로고    scopus 로고
    • Modular Invariant Partition Functions in the Quantum Hall Effect
    • Andrea Cappelli and Guillermo R. Zemba, Modular Invariant Partition Functions in the Quantum Hall Effect, Nucl. Phys. B 490, 595 (1997).
    • (1997) Nucl. Phys. B , vol.490 , pp. 595
    • Cappelli, A.1    Zemba, G.R.2
  • 32
    • 73749083094 scopus 로고    scopus 로고
    • Chiral Partition Functions of Quantum Hall Droplets
    • A. Cappelli, G. Viola, and G. R. Zemba, Chiral Partition Functions of Quantum Hall Droplets, Ann. Phys. 325, 465 (2010).
    • (2010) Ann. Phys , vol.325 , pp. 465
    • Cappelli, A.1    Viola, G.2    Zemba, G.R.3
  • 33
    • 79551657612 scopus 로고    scopus 로고
    • Partition Functions of Non-Abelian Quantum Hall States
    • Andrea Cappelli and Giovanni Viola, Partition Functions of Non-Abelian Quantum Hall States, J. Phys. A 44, 075401 (2011).
    • (2011) J. Phys. A , vol.44 , pp. 075401
    • Cappelli, A.1    Viola, G.2
  • 36
    • 33344468870 scopus 로고    scopus 로고
    • Solving Gapped Hamiltonians Locally
    • M. B. Hastings, Solving Gapped Hamiltonians Locally, Phys. Rev. B 73, 085115 (2006).
    • (2006) Phys. Rev. B , vol.73 , pp. 085115
    • Hastings, M.B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.