Entropy-driven formation of a half-quantum vortex lattice

Half-quantum vortices (HQVs) can exist in a superconductor or superfluid with an exact or approximate U(1)×U(1) symmetry, for instance, in spinor condensates, ³He-A, Sr₂RuO₄, and possibly cuprate superconductors with stripe order. In this paper, we show that a lattice of HQVs can be stabilized at finite temperature even when it does not have lower energy than the lattice of full vortices at $T=0$ since there is a gain in configurational entropy when a full vortex fractionalizes into a pair of HQVs. Specifically, the lattice of HQVs has an optical branch of phonon modes absent in the lattice of full vortices. Moreover, the HQV lattice at $T>0$ can have a different structure than the HQV lattice at $T=0$.