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

Spontaneous Breakdown of Time-Reversal Symmetry Induced by Thermal Fluctuations