Who is the Lord of the Rings: Majorana, Dirac or Lifshitz? The Spin-Orbit-Zeeman Saga in Ultra-cold Fermions

TL;DR

This paper explores topological phase transitions in ultra-cold fermionic superfluids with spin-orbit and Zeeman fields, revealing the formation of zero-energy rings and Majorana fermions, and classifying these transitions as Lifshitz types.

Contribution

It demonstrates the emergence of topological phases with zero-energy rings and characterizes Lifshitz transitions involving Majorana and Dirac fermions in ultra-cold fermions.

Findings

Rings of zero-energy excitations appear in superfluid phases.

Lifshitz class phase transitions involve Majorana and Dirac fermions.

Spectroscopic properties reveal topological changes at phase boundaries.

Abstract

We discuss the emergence of rings of zero-energy excitations in momentum space for superfluid phases of ultra-cold fermions when spin-orbit, Zeeman fields and interactions are varied. We show that phases containing rings of nodes possess non-trivial topological invariants, and that phase transitions between distinct topological phases belong to the Lifshitz class. Upon crossing phase boundaries, existing massless Dirac fermions in the gapless phase anihilate to produce bulk zero-mode Majorana fermions at phase boundaries and then become massive Dirac fermions in the gapped phase. We characterize these tunable topological phase transitions via several spectroscopic properties, including excitation spectrum, spectral function and momentum distribution. Since the emergence or disappearance of rings leads to topological transitions in momentum space, we conclude that Lifshitz is the lord of the rings.