Line Junctions in the Quantum Hall Effect

TL;DR

This paper proposes a method to observe a 1d metal-insulator transition in quantum Hall systems using a line junction, where the transition's signature is a distinct temperature dependence of conductivity.

Contribution

It introduces a novel 1d system created by a gate in fractional quantum Hall fluids, enabling tuning through a localization transition and providing a way to measure conductivity via Hall transport.

Findings

The 1d system is isomorphic to a disordered attractive electron gas.

A temperature-dependent conductivity signature indicates the metal-insulator transition.

Predictions extend to a $ u=2/3$ quantum Hall fluid.

Abstract

A long skinny gate across a fractional quantum Hall fluid at filling $\nu=1/m$ with odd integer $m$, creates a novel one-dimensional (1d) system which is isomorphic to a disordered 1d electron gas with {\it attractive} interactions. By varying the gate potential along such a line junction, it should be possible to tune through the 1d localization transition, predicted for an attractively interacting electron gas. The key signature of this 1d metal-insulator transition is the temperature dependence of the conductivity, which diverges as a power of temperature in the metallic phase, and vanishes rapidly in the insulator. We show that the 1d conductivity can be extracted from a standard Hall transport measurement, in the regime where the Hall conductance is close to its quantized value. A line junction in a $\nu=2/3$ quantized Hall fluid is predicted to exhibit a similar localization transition.