Spontaneous breakdown of time-reversal symmetry induced by thermal fluctuations

In systems with broken U (1) symmetry, such as superfluids, superconductors, or magnets, the symmetry restoration is driven by the proliferation of topological defects in the form of vortex loops (unless the phase transition is strongly first order). Here we discuss that the proliferation of topological defects can, by contrast, lead to the breakdown of an additional symmetry. We demonstrate that this effect should take place in s+is superconductors, which are widely discussed in connection with iron-based materials (although the mechanism is much more general). In these systems a vortex excitation can create a ``bubble'' of fluctuating Z₂ order parameter. The thermal excitation of vortices then leads to the breakdown of Z₂ time-reversal symmetry when the temperature is increased.