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.

29 pages, 1 figure

References in corpus (15)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• 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
• Topological Crystalline Insulators
• 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
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Surface States of the Topological Insulator Bi_{1-x}Sb_x
• The space group classification of topological band insulators
• Topology of crystalline insulators and superconductors
• Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators
• On the $Z_2$ classification of Quantum Spin Hall Models
• Surface Majorana Cone of the Superfluid ${}^3$He B Phase

Cited by in corpus (12)

• Symmetry Protected Topological Superfluid ${}^3$He-B
• Tenfold Topology of Crystals: Unified classification of crystalline topological insulators and superconductors
• Topological features of ground states and topological solitons in generalized Su-Schrieffer-Heeger models using generalized time-reversal, particle-hole, and chiral symmetries
• Fate of exceptional points under interactions: Reduction of topological classifications
• Higher-order Weyl superconductors with anisotropic Weyl-point connectivity
• 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
• C-P-T Fractionalization
• Reduction of $\mathbb{Z}$ classification of a two-dimensional weak topological insulator - real-space DMFT study -
• Modulating Hamiltonian Approach to Quantum Many-Body Systems and Crystalline Topological Phases Protected by Generalized Magnetic Translations