Mesoscopic Effects in the Fractional Quantum Hall Regime: Chiral Luttinger versus Fermi Liquid

TL;DR

This paper investigates tunneling in fractional quantum Hall edge states, revealing a crossover from Luttinger liquid to Fermi liquid behavior with temperature, and proposes experimental methods to distinguish these states.

Contribution

It extends Wen's chiral Luttinger liquid theory to include mesoscopic effects, identifying a crossover in oscillation behavior and predicting new high-temperature phenomena.

Findings

Aharonov-Bohm oscillation amplitude shows a crossover from power-law to Fermi-liquid behavior.

Amplitude exhibits a pronounced maximum near the crossover temperature.

Predicted nonlinear phenomena provide experimental signatures to distinguish Luttinger and Fermi liquids.

Abstract

We study tunneling through an edge state formed around an antidot in the fractional quantum Hall regime using Wen's chiral Luttinger liquid theory extended to include mesoscopic effects. We identify a new regime where the Aharonov-Bohm oscillation amplitude exhibits a distinctive crossover from Luttinger liquid power-law behavior to Fermi-liquid-like behavior as the temperature is increased. Near the crossover temperature the amplitude has a pronounced maximum. This non-monotonic behavior and novel high-temperature nonlinear phenomena that we also predict provide new ways to distinguish experimentally between Luttinger and Fermi liquids.