In this talk, I will present our recent work on 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_KT drives the transition from a thermal Quantum
Hall insulator to a thermal metal/insulator, and dramatically modifies the
ground-state degeneracy splitting. This shows that in order to utilize 2D
chiral p-wave superconductors for topological quantum computing, the
temperature should be much smaller than T_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.