Topology of the planar phase of superfluid ${}^3$He and bulk-boundary correspondence for three dimensional topological superconductors

Abstract

We provide topological classification of possible phases with the symmetry of the planar phase of superfluid ${}^3$He. Compared to the B-phase (class DIII in classification of Altland and Zirnbauer), it has an additional symmetry, which modifies the topology. We analyze the topology in terms of explicit mappings from the momentum space and also discuss explicitly topological invariants for the B-phase. We further show, how the bulk-boundary correspondence for the 3D B-phase can be inferred from that for the 2D planar phase. A general condition is derived for the existence of topologically stable zero modes at the surfaces of 3D superconductors with class DIII symmetries.

References in corpus (6)

• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Crystalline Insulators
• Antiferromagnetic topological insulators
• The space group classification of topological band insulators
• Four-dimensional graphene and chiral fermions
• Study of superfluid ${}^3$He under nanoscale confinement. A new approach to the investigation of superfluid ${}^3$He films

Cited by in corpus (14)

• Symmetry Protected Topological Superfluids and Superconductors --- From the Basics to ${}^3$He ---
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• Weyl and Dirac semimetals with Z_2 topological charge
• Emergent Weyl spinors in multi-fermion systems
• Symmetry Protected Topological Superfluid ${}^3$He-B
• Andreev-Majorana bound states in superfluids
• Bulk-edge correspondence, spectral flow and Atiyah-Patodi-Singer theorem for the Z2-invariant in topological insulators
• Time-reversal invariant topological superfluids in Bose-Fermi mixtures
• Non-Abelian Half-Quantum Vortices in ${}^3{P}_2$ Topological Superfluids
• From elasticity tetrads to rectangular vielbein
• Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors
• Vielbein with mixed dimensions and gravitational global monopole in the planar phase of superfluid ${}^3$He
• Topology of the ${}^3$He-A film on corrugated graphene substrate
• Two roads to antispacetime in polar distorted B phase: Kibble wall and half-quantum vortex