Fig. 1: Transport along the quantum Hall edge proximitized by a disordered superconductor.

a Electrons are launched toward the proximitized segment from an upstream electrode biased by voltage V. An electron propagating along the segment converts randomly into a hole over the distance l_A, which is controlled by disorder in the superconductor, see Eq. (8). b Evolution of the electronic wave function, see Eq. (10), is similar to the motion of a “spin” in a stochastic effective “magnetic field”. The conductance G = I/V is determined by the result of a random walk of a point on a Bloch sphere. c G is a random quantity that fluctuates upon varying the electron density n in the 2DEG (traces are simulated using Eq. (10); units of n are the same for the two plots and are otherwise arbitrary). d The loss of correlation between the values of G upon a change in n is quantified by function \({{{{{{{\mathcal{C}}}}}}}}(\delta n)\), see Eqs. (15)–(17). The origin of the correlations loss is illustrated by the divergence between two stochastic trajectories on a Bloch sphere. The “spins” corresponding to different values of n experience a different effective “magnetic field”, and thus drift apart in the course of evolution. The separation of the “spins” is slower for stronger disorder. As the result, the trace G(n) in (c) is smoother for smaller l_A.