Effect of thermal fluctuations in topological p-wave superconductors

TL;DR

This paper investigates how thermal fluctuations affect the topological stability of 2D chiral p-wave superconductors, revealing a transition driven by vortex proliferation that impacts their potential for quantum computing.

Contribution

It provides a detailed analysis of vortex effects on topological phases in spinless and spinful chiral p-wave superconductors, highlighting the temperature constraints for topological quantum computing.

Findings

Vortex-antivortex proliferation causes a transition from quantum Hall insulator to metal/insulator.

Topological degeneracy splitting is significantly affected by thermal fluctuations.

Half-quantum vortices exhibit unique topological properties in the presence of full-quantum vortices.

Abstract

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_KT drives the transition from a thermal Quantum Hall insulator to a thermal metal/insulator, and dramatically modifies the ground-state degeneracy splitting. Therefore, 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.