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

We discuss the emergence of zero-energy Majorana modes ina disordered finite-length p-wave one-dimensional superconducting ring, pierced by a magnetic flux $Phi$ tuned at an appropriate value $Phi = Phi_*$. 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 [ Phi ]$ at $Phi = Phi_*$. By monitoring the discontinuities in $ I [ Phi ]$, we map out the region in parameter space characterized by the emergence of Majorana modes in the disordered ring.