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Volumn 3, Issue 4, 2014, Pages

Non-Abelian topological order on the surface of a 3d topological superconductor from an exactly solved model

Author keywords

[No Author keywords available]

Indexed keywords

BULK ELECTRONS; EXPLICIT MODELING; QUASIPARTICLES; STRONG INTERACTION; SYMMETRIC SURFACES; TIME REVERSAL SYMMETRIES; TOPOLOGICAL ORDER; TOPOLOGICAL PHASE;

EID: 84893646808     PISSN: None     EISSN: 21603308     Source Type: Journal    
DOI: 10.1103/PhysRevX.3.041016     Document Type: Article
Times cited : (353)

References (51)
  • 1
    • 78349239882 scopus 로고    scopus 로고
    • Colloquium: Topological Insulators
    • M. Z. Hasan and C. L. Kane, Colloquium: Topological Insulators, Rev. Mod. Phys. 82, 3045 (2010).
    • (2010) Rev. Mod. Phys. , vol.82 , pp. 3045
    • Hasan, M.Z.1    Kane, C.L.2
  • 2
    • 80054934761 scopus 로고    scopus 로고
    • Topological Insulators and Superconductors
    • Xiao-Liang Qi and Shou-Cheng Zhang, Topological Insulators and Superconductors, Rev. Mod. Phys. 83, 1057 (2011).
    • (2011) Rev. Mod. Phys. , vol.83 , pp. 1057
    • Qi, X.-L.1    Zhang, S.-C.2
  • 4
    • 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
  • 5
    • 30444456387 scopus 로고    scopus 로고
    • Anyons in an Exactly Solved Model and Beyond
    • A. Kitaev, Anyons in an Exactly Solved Model and Beyond, Ann. Phys. (Amsterdam) 321, 2 (2006).
    • (2006) Ann. Phys. (Amsterdam) , vol.321 , pp. 2
    • Kitaev, A.1
  • 6
    • 79551610647 scopus 로고    scopus 로고
    • Classification of Gapped Symmetric Phases in One-Dimensional Spin Systems
    • X. Chen, Z.-C. Gu, and X.-G. Wen, Classification of Gapped Symmetric Phases in One-Dimensional Spin Systems, Phys. Rev. B 83, 035107 (2011).
    • (2011) Phys. Rev. B , vol.83 , pp. 035107
    • Chen, X.1    Gu, Z.-C.2    Wen, X.-G.3
  • 7
    • 79961067002 scopus 로고    scopus 로고
    • Topological Phases of Fermions in One Dimension
    • Lukasz Fidkowski and Alexei Kitaev, Topological Phases of Fermions in One Dimension, Phys. Rev. B 83, 075103 (2011).
    • (2011) Phys. Rev. B , vol.83 , pp. 075103
    • Fidkowski, L.1    Kitaev, A.2
  • 8
    • 79961064168 scopus 로고    scopus 로고
    • Topological Phases of One-Dimensional Fermions: An Entanglement Point of View
    • AriM. Turner, Frank Pollmann, and Erez Berg, Topological Phases of One-Dimensional Fermions: An Entanglement Point of View, Phys. Rev. B 83, 075102 (2011).
    • (2011) Phys. Rev. B , vol.83 , pp. 075102
    • Turner, A.M.1    Pollmann, F.2    Berg, E.3
  • 9
    • 84865596142 scopus 로고    scopus 로고
    • Interacting One-Dimensional Fermionic Symmetry-Protected Topological Phases
    • Evelyn Tang and Xiao-Gang Wen, Interacting One-Dimensional Fermionic Symmetry-Protected Topological Phases, Phys. Rev. Lett. 109, 096403 (2012).
    • (2012) Phys. Rev. Lett. , vol.109 , pp. 096403
    • Tang, E.1    Wen, X.-G.2
  • 10
    • 84879383626 scopus 로고    scopus 로고
    • A New Class of (2 + 1)-Dimensional Topological Superconductor with Z8 Topological Classification
    • X. L. Qi, A New Class of (2 {thorn} 1)-Dimensional Topological Superconductor with Z8 Topological Classification, New J. Phys. 15, 065002 (2013).
    • (2013) New J. Phys. , vol.15 , pp. 065002
    • Qi, X.L.1
  • 11
    • 84863329966 scopus 로고    scopus 로고
    • Interacting Topological Phases and Modular Invariance
    • S. Ryu and S. C. 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
  • 12
    • 84883312952 scopus 로고    scopus 로고
    • Interaction Effect on Topological Classification of Superconductors in Two Dimensions
    • Hong Yao and S. Ryu, Interaction Effect on Topological Classification of Superconductors in Two Dimensions, Phys. Rev. B 88, 064507 (2013).
    • (2013) Phys. Rev. B , vol.88 , pp. 064507
    • Yao, H.1    Ryu, S.2
  • 13
    • 84893678550 scopus 로고    scopus 로고
    • The Effect of Interactions on 2D Fermionic Symmetry-Protected Topological Phases with Z2 Symmetry
    • arXiv:1304.4569
    • Z. C. Gu and M. Levin, The Effect of Interactions on 2D Fermionic Symmetry-Protected Topological Phases with Z2 Symmetry, arXiv:1304.4569.
    • Gu, Z.C.1    Levin, M.2
  • 14
    • 84871441220 scopus 로고    scopus 로고
    • Symmetry-Protected Topological Orders in Interacting Bosonic Systems
    • Xie Chen, Zheng-Cheng Gu, Zheng-Xin Liu, and Xiao-Gang Wen, Symmetry-Protected Topological Orders in Interacting Bosonic Systems, Science 338, 1604 (2012)
    • (2012) Science , vol.338 , pp. 1604
    • Chen, X.1    Gu, Z.-C.2    Liu, Z.-X.3    Wen, X.-G.4
  • 15
    • 84876169194 scopus 로고    scopus 로고
    • Symmetry Protected Topological Orders and the Group Cohomology of Their Symmetry Group
    • Xie Chen, Zheng-Cheng Gu, Zheng-Xin Liu, and Xiao-Gang Wen, Symmetry Protected Topological Orders and the Group Cohomology of Their Symmetry Group, Phys. Rev. B 87, 155114 (2013).
    • (2013) Phys. Rev. B , vol.87 , pp. 155114
    • Chen, X.1    Gu, Z.-C.2    Liu, Z.-X.3    Wen, X.-G.4
  • 16
    • 84866355638 scopus 로고    scopus 로고
    • Braiding Statistics Approach to Symmetry-Protected Topological Phases
    • M. Levin and Z.-C. 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
  • 17
    • 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
  • 18
    • 84875334666 scopus 로고    scopus 로고
    • Physics of Three-Dimensional Bosonic Topological Insulators: Surface-Deconfined Criticality and Quantized Magnetoelectric Effect
    • Ashvin Vishwanath and T. Senthil, Physics of Three-Dimensional Bosonic Topological Insulators: Surface-Deconfined Criticality and Quantized Magnetoelectric Effect, Phys. Rev. X 3, 011016 (2013).
    • (2013) Phys. Rev. X , vol.3 , pp. 011016
    • Vishwanath, A.1    Senthil, T.2
  • 19
    • 84877041962 scopus 로고    scopus 로고
    • Three-Dimensional Symmetry Protected Topological Phase Close to Antiferromagnetic Néel Order
    • Cenke Xu Three-Dimensional Symmetry Protected Topological Phase Close to Antiferromagnetic Néel Order, Phys. Rev. B 87, 144421 (2013).
    • (2013) Phys. Rev. B , vol.87 , pp. 144421
    • Xu., C.1
  • 20
    • 84880831109 scopus 로고    scopus 로고
    • Bosonic Topological Insulator in Three Dimensions and the Statistical Witten Effect
    • M. Metlitski, C. L. Kane, and M. P. A. Fisher, Bosonic Topological Insulator in Three Dimensions and the Statistical Witten Effect, Phys. Rev. B 88, 035131 (2013).
    • (2013) Phys. Rev. B , vol.88 , pp. 035131
    • Metlitski, M.1    Kane, C.L.2    Fisher, M.P.A.3
  • 21
    • 84879730659 scopus 로고    scopus 로고
    • Boson Topological Insulators: A Window into Highly Entangled Quantum Phases
    • C. Wang and T. Senthil, Boson Topological Insulators: A Window into Highly Entangled Quantum Phases, Phys. Rev. B 87, 235122 (2013).
    • (2013) Phys. Rev. B , vol.87 , pp. 235122
    • Wang, C.1    Senthil, T.2
  • 22
    • 84906991437 scopus 로고    scopus 로고
    • Exactly Soluble Model of a 3D Symmetry Protected Topological Phase of Bosons with Surface Topological Order
    • arXiv:1302.7072
    • F. J. Burnell, X. Chen, L. Fidkowski, and A. Vishwanath, Exactly Soluble Model of a 3D Symmetry Protected Topological Phase of Bosons with Surface Topological Order, arXiv:1302.7072.
    • Burnell, F.J.1    Chen, X.2    Fidkowski, L.3    Vishwanath, A.4
  • 23
    • 65649108305 scopus 로고    scopus 로고
    • in Periodic Table for Topological Insulators and Superconductors
    • edited by V. Lebedev and M. Feigel'Man, American Institute of Physics Conference Series (AIP, New York, 2009)
    • A. Kitaev, in Periodic Table for Topological Insulators and Superconductors, edited by V. Lebedev and M. Feigel'Man, American Institute of Physics Conference Series Vol. 1134 (AIP, New York, 2009), pp. 22-30.
    • , vol.1134 , pp. 22-30
    • Kitaev, A.1
  • 24
    • 14944373681 scopus 로고
    • Superconductivity with Pairs in a Relative p Wave
    • R. Balian and N. R. Werthamer, Superconductivity with Pairs in a Relative p Wave, Phys. Rev. 131, 1553 (1963).
    • (1963) Phys. Rev. , vol.131 , pp. 1553
    • Balian, R.1    Werthamer, N.R.2
  • 25
    • 84922215868 scopus 로고    scopus 로고
    • The Universe in a Helium Droplet
    • (Oxford University Press, New York, 2009) ISBN 9780199564842
    • G. E. Volovik, The Universe in a Helium Droplet, International Series of Monographs on Physics (Oxford University Press, New York, 2009), ISBN 9780199564842.
    • International Series of Monographs on Physics
    • Volovik, G.E.1
  • 26
    • 1842460762 scopus 로고
    • Nonabelions in the Fractional Quantum Hall Effect
    • Gregory Moore and Nicholas Read, Nonabelions in the Fractional Quantum Hall Effect, Nucl. Phys. B 360, 362 (1991).
    • (1991) Nucl. Phys. B , vol.360 , pp. 362
    • Moore, G.1    Read, N.2
  • 27
    • 84893685009 scopus 로고    scopus 로고
    • However, a related theory, where one reverses the direction of the Majorana mode, can be made T invariant. Since this may have an application to 3D topological insulators, it will be discussed in a separate publication
    • However, a related theory, where one reverses the direction of the Majorana mode, can be made T invariant. Since this may have an application to 3D topological insulators, it will be discussed in a separate publication.
  • 28
    • 84893662946 scopus 로고    scopus 로고
    • private communication
    • Z. Wang (private communication).
    • Wang, Z.1
  • 29
    • 84893640385 scopus 로고    scopus 로고
    • Ph.D. thesis, California Institute of Technology
    • P. Bonderson, Ph.D. thesis, California Institute of Technology, 2007, http://thesis.library .caltech.edu/2447.
    • (2007)
    • Bonderson, P.1
  • 30
    • 84858624019 scopus 로고    scopus 로고
    • (3 + 1)-TQFTs and Topological Insulators Front
    • K. Walker and Z. Wang (3 {thorn} 1)-TQFTs and Topological Insulators Front. Phys. 7, 150 (2012).
    • (2012) Phys , vol.7 , pp. 150
    • Walker, K.1    Wang, Z.2
  • 31
    • 84872892560 scopus 로고    scopus 로고
    • Three-Dimensional Topological Lattice Models with Surface Anyons
    • C.W. von Keyserlingk, F. J. Burnell, and S. H. Simon Three-Dimensional Topological Lattice Models with Surface Anyons, Phys. Rev. B 87, 045107 (2013).
    • (2013) Phys. Rev. B , vol.87 , pp. 045107
    • von Keyserlingk, C.W.1    Burnell, F.J.2    Simon, S.H.3
  • 32
    • 84893645922 scopus 로고    scopus 로고
    • A. Kitaev, http://online.kitp.ucsb.edu/online/topomat11/ kitaev.
    • Kitaev, A.1
  • 33
    • 14644388676 scopus 로고
    • Quantum Field Theory and the Jones Polynomial
    • Edward Witten, Quantum Field Theory and the Jones Polynomial, Commun. Math. Phys. 121, 351 (1989).
    • (1989) Commun. Math. Phys. , vol.121 , pp. 351
    • Witten, E.1
  • 34
    • 0000011912 scopus 로고    scopus 로고
    • Beyond Paired Quantum Hall States: Parafermions and Incompressible States in the First Excited Landau Level
    • N. Read and E. Rezayi, Beyond Paired Quantum Hall States: Parafermions and Incompressible States in the First Excited Landau Level, Phys. Rev. B 59, 8084 (1999).
    • (1999) Phys. Rev. B , vol.59 , pp. 8084
    • Read, N.1    Rezayi, E.2
  • 35
    • 84893699288 scopus 로고    scopus 로고
    • Sometimes, only theories with k = 0 mod 4 are labeled SO(3)k, since otherwise they are nonmodular. Since we are specifically interested in theories that contain the electron, which are necessarily nonmodular, we will not make this distinction
    • Sometimes, only theories with k = 0 mod 4 are labeled SO{eth}3{Thorn}k, since otherwise they are nonmodular. Since we are specifically interested in theories that contain the electron, which are necessarily nonmodular, we will not make this distinction.
  • 36
    • 84893652373 scopus 로고    scopus 로고
    • This structure is reminiscent of the notion of G action in a braided G-crossed category [37,38]
    • This structure is reminiscent of the notion of G action in a braided G-crossed category [37,38]
  • 37
  • 39
    • 84893684960 scopus 로고    scopus 로고
    • Symmetry Protected Topological Phases from Decorated Domain Walls
    • arXiv:1303.4301
    • X. Chen, Y.-M. Lu, and A. Vishwanath, Symmetry Protected Topological Phases from Decorated Domain Walls, arXiv:1303.4301.
    • Chen, X.1    Lu, Y.-M.2    Vishwanath, A.3
  • 40
    • 84893678050 scopus 로고    scopus 로고
    • It is actually known that the symmetric center Z(C) of any braided fusion category C comes in two types [41]: Either it consists entirely of bosons and is isomorphic to the set of representations of some finite group G, in which case the bulk forms a (possibly twisted) G-gauge theory, or it is a supersymmetric version of this, where G contains some odd elements and the corresponding representations have even and odd sectors, corresponding to bosons and fermions, respectively
    • It is actually known that the symmetric center Z(C) of any braided fusion category C comes in two types [41]: Either it consists entirely of bosons and is isomorphic to the set of representations of some finite group G, in which case the bulk forms a (possibly twisted) G-gauge theory, or it is a supersymmetric version of this, where G contains some odd elements and the corresponding representations have even and odd sectors, corresponding to bosons and fermions, respectively
  • 42
    • 84893711764 scopus 로고    scopus 로고
    • Indeed, if we take a gauge transformation to act by phase factor βca,b on the fusion space vca,b, then any choice that satisfies βss,s βss,s = i, βss,s βss,s =-i, βss,s βss,s = -i, βss,s βss,s =-i and sets the other βabc to be trivial does the trick. The action of T is then truly onsite
    • c to be trivial does the trick. The action of T is then truly onsite.
  • 44
    • 84884209202 scopus 로고    scopus 로고
    • Symmetry Enforced Non-Abelian Topological Order at the Surface of a Topological Insulator
    • arXiv:1306.3250
    • X. Chen, L. Fidkowski, and A. Vishwanath, Symmetry Enforced Non-Abelian Topological Order at the Surface of a Topological Insulator, arXiv:1306.3250.
    • Chen, X.1    Fidkowski, L.2    Vishwanath, A.3
  • 45
    • 84893688934 scopus 로고    scopus 로고
    • A pair of particles that are interchanged by T and have mutual statistics η=±1 will, when fused together, carry T2 =η This may be understood by regarding the action of T2 as taking one particle around the other
    • 2 as taking one particle around the other
  • 46
    • 84888588418 scopus 로고    scopus 로고
    • Symmetry-Protected Topological Orders for Interacting Fermions-Fermionic Topological Non-linear Sigma-Models and a Group Super-cohomology Theory
    • arXiv:1201.2648
    • Z. C. Gu and X.-G. Wen, Symmetry-Protected Topological Orders for Interacting Fermions-Fermionic Topological Non-linear Sigma-Models and a Group Super-cohomology Theory, arXiv:1201.2648.
    • Gu, Z.C.1    Wen, X.-G.2
  • 47
    • 84884206187 scopus 로고    scopus 로고
    • A Symmetry-Respecting Topologically-Ordered Surface Phase of 3D Electron Topological Insulators
    • arXiv:1306.3286
    • M. A. Metlitski, C. L. Kane, and M. P. A. Fisher, A Symmetry-Respecting Topologically-Ordered Surface Phase of 3D Electron Topological Insulators, arXiv:1306.3286.
    • Metlitski, M.A.1    Kane, C.L.2    Fisher, M.P.A.3
  • 48
    • 84884203116 scopus 로고    scopus 로고
    • Gapped Symmetry Preserving Surface-State for the Electron Topological Insulator
    • arXiv:1306.3238
    • C. Wang, A. C. Potter, and T. Senthil, Gapped Symmetry Preserving Surface-State for the Electron Topological Insulator, arXiv:1306.3238.
    • Wang, C.1    Potter, A.C.2    Senthil, T.3
  • 49
    • 67650302046 scopus 로고    scopus 로고
    • Time-Reversal-Invariant Topological Superconductors and Superfluids in Two and Three Dimensions
    • Xiao-Liang Qi, Taylor L. Hughes, S. Raghu, and Shou-Cheng Zhang, Time-Reversal-Invariant Topological Superconductors and Superfluids in Two and Three Dimensions, Phys. Rev. Lett., 102, 187001 (2009).
    • (2009) Phys. Rev. Lett. , vol.102 , pp. 187001
    • Qi, X.-L.1    Hughes, T.L.2    Raghu, S.3    Zhang, S.-C.4
  • 50
    • 84893658310 scopus 로고    scopus 로고
    • Classification Properties of Symmetry Enriched Topological Phases: A Chern-Simons Approach with Applications to Z2 Spin Liquids
    • arXiv:1302.2634
    • Y.-M. Lu and A. Vishwanath, Classification and Properties of Symmetry Enriched Topological Phases: A Chern-Simons Approach with Applications to Z2 Spin Liquids, arXiv:1302.2634.
    • Lu, Y.-M.1    Vishwanath, A.2
  • 51
    • 84893711948 scopus 로고    scopus 로고
    • Related results have been obtained by C. Wang, A. Potter, and T. Senthil (unpublished) in the context of topological insulators
    • Related results have been obtained by C. Wang, A. Potter, and T. Senthil (unpublished) in the context of topological insulators.


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