Resistance Distribution of Decoherent Quantum Hall-Superconductor Edges

We study the probability distribution of the resistance, or equivalently the charge transmission, of a decoherent quantum Hall-superconductor edge, with the decoherence coming from metallic puddles along the edge. Such metallic puddles may originate from magnetic vortex cores or other superconductivity suppressing perturbations. In contrast to the distribution of a coherent edge which is peaked away from zero charge transmission, we show analytically and numerically that the distribution of a decoherent edge with metallic puddles is always peaked at zero charge transmission, which serves as a probe of coherence of superconducting chiral edge states. We further show that the distribution width decays exponentially in magnetic field and temperature. Our theoretical decoherent distribution agrees well with the recent experimental observation in graphene with superconducting proximity.