Persistent current and zero-energy Majorana modes in a p -wave disordered superconducting ring

Abstract

We discuss the emergence of zero-energy Majorana modes in a disordered finite-length $p$-wave one-dimensional superconducting ring, pierced by a magnetic flux $\mathrm{\ensuremath{\Phi}}$ tuned at an appropriate value $\mathrm{\ensuremath{\Phi}}={\mathrm{\ensuremath{\Phi}}}_{*}$. In the absence of fermion parity conservation, we evidence the emergence of the Majorana modes by looking at the discontinuities in the persistent current $I[\mathrm{\ensuremath{\Phi}}]$ at $\mathrm{\ensuremath{\Phi}}={\mathrm{\ensuremath{\Phi}}}_{*}$. By monitoring the discontinuities in $I[\mathrm{\ensuremath{\Phi}}]$, we map out the region in parameter space characterized by the emergence of Majorana modes in the disordered ring.