On transport in quantum Hall systems with constrictions

TL;DR

This paper models transport in quantum Hall systems with constrictions, explaining experimental puzzles through a hydrodynamic theory of edge modes and tunneling processes that influence conductance.

Contribution

It introduces a phenomenological model linking edge excitations and tunneling processes to transport behavior in quantum Hall constrictions.

Findings

Matching edge properties explains backscattering.

Competition between tunneling processes affects conductance.

The model aligns with recent experimental observations.

Abstract

Motivated by recent experimental findings, we study transport in a simple phenomenological model of a quantum Hall edge system with a gate-voltage controlled constriction lowering the local filling factor. The current backscattered from the constriction is seen to arise from the matching of the properties of the edge-current excitations in the constriction ($\nu_{2}$) and bulk ($\nu_{1}$) regions. We develop a hydrodynamic theory for bosonic edge modes inspired by this model, finding that a competition between two tunneling process, related by a quasiparticle-quasihole symmetry, determines the fate of the low-bias transmission conductance. In this way, we find satisfactory explanations for many recent puzzling experimental results.