Evolution of edge states in topological superfluids during the quantum phase transition

Abstract

The quantum phase transition between topological and non-topological insulators or between fully gapped superfluids/superconductors can occur without closing the gap. We consider the evolution of the Majorana edge states on the surface of topological superconductor during transition to the topologically trivial superconductor on example of non-interacting Hamiltonian describing the spin-triplet superfluid 3He-B. In conventional situation when the gap is nullified at the transition, the spectrum of Majorana fermions shrinks and vanishes after the transition to the trivial state. If the topological transition occurs without the gap closing, the Majorana fermion spectrum disappears by escaping to ultraviolet, where Green's function approaches zero. This demonstrates the close connection between the topological transition without closing the gap and zeroes in the Green's function. Similar connection takes place in interacting systems where zeroes may occur due to interaction.

5 pages, 2 figures, JETP Letters style, version submitted to JETP Letters

References in corpus (7)

• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Lattice model of three-dimensional topological singlet superconductor with time-reversal symmetry
• Majorana surface states of superfluid 3He A- and B-phases in a slab
• Topological superfluid ${}^3$He-B: fermion zero modes on interfaces and in the vortex core
• Anomalous Attenuation of Transverse Sound in 3He
• Pairing symmetry and vortex zero-mode for superconducting Dirac fermions

Cited by in corpus (9)

• Topological invariants and interacting one-dimensional fermionic systems
• Symmetry Protected Topological Superfluids and Superconductors --- From the Basics to ${}^3$He ---
• Symmetry Protected Topological Superfluid ${}^3$He-B
• Andreev-Majorana bound states in superfluids
• Momentum space topological invariants for the 4D relativistic vacua with mass gap
• Generalized unparticles, zeros of the Green function, and momentum space topology of the lattice model with overlap fermions
• Massive Dirac fermions from holography
• Momentum space topology in the lattice gauge theory
• Internal wave crystals