We study the effect of thermal fluctuations on the topological stability of chiral $p$-wave superconductors. We consider two models of superconductors: spinless and spinful with a focus on topological properties and Majorana zero-energy modes. We show that proliferation of vortex-antivortex pairs above the Kosterlitz-Thouless temperature $T_{\mathrm{KT}}$ drives the transition from a thermal quantum hall insulator to a thermal metal/insulator, and dramatically modifies the ground-state degeneracy splitting. Therefore, to utilize two-dimensional chiral $p$-wave superconductors for topological quantum computing, the temperature should be much smaller than $T_{\mathrm{KT}}$. Within the spinful chiral $p$-wave model, we also investigate the interplay between half-quantum vortices carrying Majorana zero-energy modes and full-quantum vortices having trivial topological charge, and discuss topological properties of half-quantum vortices in the background of proliferating full-quantum vortices.

• Received 11 June 2012

DOI:https://doi.org/10.1103/PhysRevB.87.014503