Ballistic-to-diffusive transition in engineered counter-propagating quantum Hall channels

TL;DR

This study investigates how charge transport in engineered quantum Hall systems with counter-propagating edge states transitions from ballistic to diffusive regimes, depending on the number of channels and their coupling.

Contribution

It demonstrates controlled tuning of charge equilibration and reveals a transition from ballistic to diffusive transport in engineered quantum Hall channels.

Findings

Ballistic transport occurs with unequal numbers of counter-propagating channels.

A critical diffusive regime emerges with equal numbers of channels, marked by diverging equilibration length.

The method enables simulation of exotic quantum Hall effects with adjustable parameters.

Abstract

Exotic quantum Hall systems hosting counter-propagating edge states can show seemingly non-universal transport regimes, usually depending on the size of the sample. We experimentally probe transport in a quantum Hall sample engineered to host a tunable number of counter-propagating edge states. The latter are coupled by Landauer reservoirs, which force charge equilibration over a tunable effective length. We show that charge transport is determined by the balance of up- and downstream channels, with a ballistic regime emerging for unequal numbers of channels. For equal numbers, we observe a transition to a critical diffusive regime, characterized by a diverging equilibration length. Our approach allows simulating the equilibration of hole-conjugate states and other exotic quantum Hall effects with fully controlled parameters using well-understood quantum Hall states.