Disorder-enabled Andreev reflection of a quantum Hall edge

We develop a theory of charge transport along the quantum Hall edge proximitized by a superconductor. We note that generically Andreev reflection of an edge state is suppressed if translation invariance along the edge is preserved. Disorder in a “dirty” superconductor enables the Andreev reflection but makes it random. As a result, the conductance of a proximitized segment is a stochastic quantity with giant sign-alternating fluctuations and zero average. We find the statistical distribution of the conductance and its dependence on electron density, magnetic field, and temperature. Our theory provides an explanation of a recent experiment with a proximitized edge state. The properties of edge states at the boundary between a quantum Hall insulator and a superconductor have recently been under scrutiny. Here, the authors find theoretically that Andreev reflection of an edge state is possible only if the superconductor is in the disordered limit, leading to stochastic edge state conductance and providing an explanation of a recent experiment.