Spontaneous Breakdown of Time-Reversal Symmetry Induced by Thermal Fluctuations

TL;DR

This paper explores how thermal fluctuations and vortex proliferation in $s+is$ superconductors can spontaneously break time-reversal symmetry, revealing a novel mechanism distinct from traditional symmetry restoration in superfluids and magnets.

Contribution

It demonstrates that vortex-induced topological defect proliferation can cause $Z_2$ symmetry breaking in $s+is$ superconductors, a phenomenon not previously identified.

Findings

Thermal vortex excitations create $Z_2$ order parameter bubbles.

Increasing temperature leads to $Z_2$ symmetry breakdown.

The mechanism differs from symmetry restoration in other systems.

Abstract

In systems with broken $U(1)$ symmetry, such as superfluids, superconductors or magnets, the symmetry restoration is driven by proliferation of topological defects in the form of vortex loops. Here we discuss that in certain systems the proliferation of topological defects can, by contrast, lead to the breakdown of an additional symmetry. As a particular example we demonstrate that this effect should take place in $s+is$ superconductors, which are widely discussed in connection with the Iron-based materials. In these systems a vortex excitation can create a "bubble" of fluctuating $Z_2$ order parameter. Thermal excitation of vortices then leads to breakdown of $Z_2$ time-reversal symmetry when the temperature is increased.