Localization and conductance in fractional quantum Hall edges

TL;DR

This paper develops a theoretical framework to analyze how Anderson localization affects transport in fractional quantum Hall edge states, including counter-propagating modes, relevant for recent experimental setups.

Contribution

It introduces a general method for calculating conductance in localized FQH edges, encompassing various geometries and regimes, advancing understanding of edge transport phenomena.

Findings

Derived a general conductance formula incorporating localization effects.

Analyzed transport in experimentally relevant FQH edge geometries.

Provided insights into the impact of counter-propagating modes on conductance.

Abstract

The fractional quantum Hall (FQH) effect gives rise to abundant topological phases, presenting an ultimate platform for studying the transport of edge states. Generic FQH edge contains multiple edge modes, commonly including the counter-propagating ones. A question of the influence of Anderson localization on transport through such edges arises. Recent experimental advances in engineering novel devices with interfaces of different FQH states enable transport measurements of FQH edges and edge junctions also featuring counter-propagating modes. These developments provide an additional strong motivation for the theoretical study of the effects of localization on generic edge states. We develop a general framework for analyzing transport in various regimes that also naturally includes localization. Using a reduced field theory of the edge after localization, we derive a general formula for the conductance. We apply this framework to analyze various experimentally relevant geometries of FQH edges and edge junctions.