Optical spin transport theory of spin-1/2 topological Fermi superfluids

TL;DR

This paper develops a theoretical framework to analyze optical spin transport in a one-dimensional topological superfluid of spin-1/2 particles, revealing how spin conductivity signals topological phase transitions and Majorana modes.

Contribution

It introduces a BCS-Leggett based model for spin transport in topological superfluids, connecting many-body physics with topological phase transitions and Majorana zero modes.

Findings

Optical spin conductivity exhibits a spin gap in the trivial phase.

The spin gap closes at the topological phase transition.

The low-energy Majorana mode model's validity is discussed across the BCS-BEC crossover.

Abstract

We theoretically investigate optical (frequency-dependent) bulk spin transport properties in a spin-1/2 topological Fermi superfluid. We specifically consider a one-dimensional system with an interspin {\it p}-wave interaction, which can be realized in ultracold atom experiments. Developing the BCS-Leggett theory to describe the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensate (BEC) evolution and the $\mathbb{Z}_2$ topological phase transition in this system, we show how the spin transport reflects these many-body aspects. We find that the optical spin conductivity, which is a small AC response of a spin current, shows the spin gapped spectrum in the wide parameter region and the gap closes at $\mathbb{Z}_2$ topological phase transition point. Moreover, the validity of the low-energy effective model of the Majorana zero mode is discussed along the BCS-BEC evolution in connection with the scale invariance at {\it p}-wave unitarity.