Topological phases of quasi-one-dimensional fermionic atoms with a synthetic gauge field

TL;DR

This paper explores how intertube tunneling affects topological superfluid phases in quasi-one-dimensional fermionic gases with spin-orbit coupling, revealing conditions for Majorana zero modes to persist.

Contribution

It introduces a new topological number based on hidden mirror symmetry that predicts Majorana modes survive intertube tunneling in certain configurations.

Findings

Majorana modes can survive intertube tunneling with an odd number of tubes.

A new topological number guarantees the existence of Majorana zero modes.

The results generalize to nanowire topological superconductors.

Abstract

We theoretically investigate the effect of intertube tunneling in topological superfluid phases of a quasi-one-dimensional Fermi gas with a Rashba-type spin-orbit interaction. It is shown that the effective Hamiltonian is analogous to that of a nanowire topological superconductor with multibands. Using a hidden mirror symmetry in the system, we introduce a new topological number that ensures the existence of non-Abelian Majorana zero modes even in the presence of intertube tunneling. It is demonstrated from the full numerical calculation of self-consistent equations that some of Majorana modes survive against the intertube tunneling, when the number of one-dimensional tubes is odd in the $y$-direction. We also discuss a generalization of our consideration to nanowire topological superconductors.