Crossed Andreev reflection of a quantum Hall edge

We develop the theory of charge transport along the quantum Hall edge proximitized by a superconductor. An electron incident on the proximitized segment of the edge may be transmitted across it either normally or, upon experiencing an Andreev reflection, as a hole. The amplitudes of these processes are sensitive to disorder in the structure, which leads to large mesoscopic fluctuations of the segment’s transconductance with magnetic field and carrier concentration. We show that, for a long segment, the fluctuations are alternating in sign and have a zero mean. We quantify the dependence of the average conductance, its variance and correlation function on the length of the proximitized segment, as well as on properties on the superconducting electrode and the NS interface. Our analytical theory explains key observations of a recent experiment [L. Zhao et. al., Nature Physics 16, 862 (2020)].