Spontaneous breaking of time-reversal symmetry in topological superconductors

TL;DR

This paper investigates how topological superconductors with direction-dependent phases can spontaneously break time-reversal symmetry, leading to nontrivial topological states characterized by Chern numbers and chiral edge modes.

Contribution

It demonstrates that phase differences in superconducting order parameters induce topological states with spontaneous time-reversal symmetry breaking.

Findings

Topological superconducting states with nontrivial Chern numbers are realized.

Spontaneous breaking of time-reversal symmetry occurs at the phase transition.

Chiral gapless edge modes exhibit unique behaviors in these states.

Abstract

We study the behavior of spinless fermions in superconducting state, in which the phases of the superconducting order parameter depend on the direction of the link. We find that the energy of the superconductor depends on the phase differences of the superconducting order parameter. The solutions for the phases corresponding to the energy minimuma, lead to a topological superconducting state with the nontrivial Chern numbers. We focus our quantitative analysis on the properties of topological states of superconductors with different crystalline symmetry and show that the phase transition in the topological superconducting state is result of spontaneous breaking of time-reversal symmetry in the superconducting state. The peculiarities in the chiral gapless edge modes behavior are studied, the Chern numbers are calculated.