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

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 ? tuned at an appropriate value ?=?*. 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[?] at ?=?*. By monitoring the discontinuities in I[?], we map out the region in parameter space characterized by the emergence of Majorana modes in the disordered ring.