CPT theorem and classification of topological insulators and superconductors

Abstract

We present a systematic topological classification of fermionic and bosonic topological phases protected by time-reversal, particle-hole, parity, and combination of these symmetries. We use two complementary approaches: one in terms of K-theory classification of gapped quadratic fermion theories with symmetries, and the other in terms of the K-matrix theory description of the edge theory of (2+1)-dimensional bulk theories. The first approach is specific to free fermion theories in general spatial dimensions while the second approach is limited to two spatial dimensions but incorporates effects of interactions. We also clarify the role of CPT theorem in classification of symmetry-protected topological phases, and show, in particular, topological superconductors dis- cussed before are related by CPT theorem.

arXiv comment29 pages, 1 figure

References in corpus (56)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect in Graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Topological Insulators in Three Dimensions
• Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Topological invariants of time-reversal-invariant band structures
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Topological Crystalline Insulators
• Periodic table for topological insulators and superconductors
• Topological Crystalline Insulators in the SnTe Material Class
• First direct observation of Spin-textures in Topological Insulators : Spin-resolved ARPES as a probe of topological quantum spin Hall effect and Berry's phase
• Calculation of reduced density matrices from correlation functions
• Experimental realization of a topological crystalline insulator in SnTe
• Topological phases of fermions in one dimension
• Topological crystalline insulator states in Pb(1-x)Sn(x)Se
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Surface States of the Topological Insulator Bi_{1-x}Sb_x
• A topological crystalline insulator (TCI) phase via topological phase transition and crystalline mirror symmetry
• The space group classification of topological band insulators
• The effects of interactions on the topological classification of free fermion systems
• Topological Phases of One-Dimensional Fermions: An Entanglement Point of View
• Inversion Symmetric Topological Insulators
• Topology of crystalline insulators and superconductors
• Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators
• Theory and classification of interacting 'integer' topological phases in two dimensions: A Chern-Simons approach
• Classification of topological insulators and superconductors in the presence of reflection symmetry
• Fractional topological insulators
• On the $Z_2$ classification of Quantum Spin Hall Models
• Quantized Response and Topology of Insulators with Inversion Symmetry
• Topological classification with additional symmetries from Clifford algebras
• Absence of topological insulator phases in non-Hermitian PT-symmetric Hamiltonians
• Interacting topological phases and modular invariance
• Topological Mirror Superconductivity
• Classification of Two Dimensional Topological Crystalline Superconductors and Majorana Bound States at Disclinations
• Classification and analysis of two dimensional abelian fractional topological insulators
• Fractional topological liquids with time-reversal symmetry and their lattice realization
• Stability of Chiral Luttinger Liquids and Abelian Quantum Hall States.
• Majorana Fermions and Disclinations in Topological Crystalline Superconductors
• Interaction effect on topological classification of superconductors in two dimensions
• Symmetry-Protected Majorana Fermions in Topological Crystalline Superconductors: Theory and Application to Sr2RuO4
• Chiral Topological Insulators, Superconductors and other competing orders in three dimensions
• Wire deconstructionism of two-dimensional topological phases
• A new class of $(2+1)$-d topological superconductor with ${\mathbb{Z}}_8$ topological classification
• New class of topological superconductors protected by magnetic group symmetries
• Entanglement Spectrum Classification of $C_n$-invariant Noninteracting Topological Insulators in Two Dimensions
• Surface Majorana Cone of the Superfluid ${}^3$He B Phase
• Time-reversal symmetric hierarchy of fractional incompressible liquids
• Topological phases of quasi-one-dimensional fermionic atoms with a synthetic gauge field
• Symmetry-protected entangling boundary zero modes in crystalline topological insulators

Cited by in corpus (37)

• Classification of topological quantum matter with symmetries
• Non-Hermitian perspective of the band structure in heavy-fermion systems
• Topological phases protected by point group symmetry
• Building crystalline topological phases from lower-dimensional states
• Gauging spatial symmetries and the classification of topological crystalline phases
• Symmetry Protected Topological Superfluids and Superconductors --- From the Basics to ${}^3$He ---
• Many-body topological invariants for fermionic short-range entangled topological phases protected by antiunitary symmetries
• Reflection and time reversal symmetry enriched topological phases of matter: path integrals, non-orientable manifolds, and anomalies
• Crystalline topological phases as defect networks
• Global anomalies on the surface of fermionic symmetry-protected topological phases in (3+1) dimensions
• Classification of Crystalline Topological Insulators and Superconductors with Point Group Symmetries
• Chiral-symmetry protected exceptional torus in correlated nodal-line semi-metals
• Generalized homology and Atiyah-Hirzebruch spectral sequence in crystalline symmetry protected topological phenomena
• Minimalist approach to the classification of symmetry protected topological phases
• Exceptional band touching for strongly correlated systems in equilibrium
• Symmetry Protected Topological Superfluid ${}^3$He-B
• Tenfold Topology of Crystals: Unified classification of crystalline topological insulators and superconductors
• Topological and non-topological features of generalized Su-Schrieffer-Heeger models
• Topological features of ground states and topological solitons in generalized Su-Schrieffer-Heeger models using generalized time-reversal, particle-hole, and chiral symmetries
• Correlation effects on topological crystalline insulators
• Fate of Majorana modes in ${\mathrm{CeCoIn}}_5$/${\mathrm{YbCoIn}}_5$ superlattices -a test bed for reduction of topological classification-
• Fate of exceptional points under interactions: Reduction of topological classifications
• Topological Phases on Non-orientable Surfaces: Twisting by Parity Symmetry
• Reduction of topological $\mathbb{Z}$ classification in cold atomic systems
• Higher-order Weyl superconductors with anisotropic Weyl-point connectivity
• Organizing symmetry-protected topological phases by layering and symmetry reduction: a minimalist perspective
• Bosonic symmetry protected topological phases with reflection symmetry
• Surface field theories of point group symmetry protected topological phases
• Commuting-projector Hamiltonians for 2D topological insulators: edge physics and many-body invariants
• Protected Gapless Edge States In Trivial Topology
• Rigidity of topological invariants to symmetry breakings
• Lieb-Schultz-Mattis Theorem for 1D Quantum Magnets with Antiunitary Translation and Inversion Symmetries
• Stability of Topological Insulators with Non-Abelian Edge Excitations
• Topological properties of magnetically ordered heavy-fermion systems in the presence of mirror symmetry
• Reduction of $\mathbb{Z}$ classification of a two-dimensional weak topological insulator - real-space DMFT study -
• C-P-T Fractionalization
• Modulating Hamiltonian Approach to Quantum Many-Body Systems and Crystalline Topological Phases Protected by Generalized Magnetic Translations