Poissonian tunneling through an extended impurity in the quantum Hall effect

TL;DR

This paper analyzes Poissonian tunneling in quantum Hall edge states with arbitrary extended impurities, deriving general relations for current and noise, and revealing interference effects in conductance.

Contribution

It provides a general analytical framework for tunneling through extended impurities in quantum Hall systems, including interference effects and a renormalized tunneling amplitude.

Findings

Schottky relation holds for arbitrary tunneling potentials.

Derived analytical expression for backscattering current with voltage-dependent renormalization.

Extended contact causes interference, suppressing differential conductance and producing anomalous bias dependence.

Abstract

We consider transport in the Poissonian regime between edge states in the quantum Hall effect. The backscattering potential is assumed to be arbitrary, as it allows for multiple tunneling paths. We show that the Schottky relation between the backscattering current and noise can be established in full generality: the Fano factor corresponds to the electron charge (the quasiparticle charge) in the integer (fractional) quantum Hall effect, as in the case of purely local tunneling. We derive an analytical expression for the backscattering current, which can be written as that of a local tunneling current, albeit with a renormalized tunneling amplitude which depends on the voltage bias. We apply our results to a separable tunneling amplitude which can represent an extended point contact in the integer or in the fractional quantum Hall effect. We show that the differential conductance of an extended quantum point contact is suppressed by the interference between tunneling paths, and it has an anomalous dependence with respect to the bias voltage.