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

TL;DR

This paper investigates how Majorana edge states evolve during topological phase transitions in superfluids, especially when the transition occurs without closing the energy gap, revealing a connection to Green's function zeros.

Contribution

It demonstrates the evolution of Majorana edge states during topological transitions without gap closing, linking this phenomenon to Green's function zeros in both non-interacting and interacting systems.

Findings

Majorana spectrum vanishes by escaping to ultraviolet during gapless transition

Topological transition without gap closing involves Green's function zeros

Zeroes in Green's function are connected to topological phase changes

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.