# Finite temperature effects on Majorana bound states in chiral $p$-wave superconductors

## TL;DR

This paper investigates how finite temperatures affect Majorana bound states in chiral p-wave superconductors, revealing that thermal effects cause algebraic decay in fermionic parity differences, but zero-temperature properties are recoverable below the minigap.

## Contribution

It provides a detailed analysis of thermal effects on Majorana states, showing how temperature influences their stability and potential for quantum computing applications.

## Key findings

- Thermal occupation causes algebraic decay of fermionic parity differences.
- Zero-temperature properties are recovered below the minigap.
- Temperatures above the minigap may still be compatible with topological quantum computation.

## Abstract

We study Majorana fermions bound to vortex cores in a chiral $p$-wave superconductor at temperatures non-negligible compared to the superconducting gap. Thermal occupation of Caroli de Gennes-Matricon states, below the full gap, causes the free energy difference between the two fermionic parity sectors to decay algebraically with increasing temperature. The power law acquires an additional factor of $T^{-1}$ for each bound state thermally excited. The zero-temperature result is exponentially recovered well below the minigap (lowest-lying CdGM level). Our results suggest that temperatures larger than the minigap may not be disastrous for topological quantum computation. We discuss the prospect of precision measurements of pinning forces on vortices as a readout scheme for Majorana qubits.