The Universal Edge Physics in Fractional Quantum Hall Liquids

TL;DR

This paper investigates the conditions under which the universal edge tunneling behavior predicted by chiral Luttinger liquid theory can be observed in fractional quantum Hall systems, highlighting the advantages of graphene-based devices.

Contribution

It identifies parameter regimes in graphene devices that prevent edge reconstruction, enabling experimental verification of universal edge tunneling exponents.

Findings

Graphene devices can access parameters avoiding edge reconstruction.

Edge reconstruction affects the tunneling exponent in fractional quantum Hall edges.

Graphene-based systems are suitable for testing universal edge physics.

Abstract

The chiral Luttinger liquid theory for fractional quantum Hall edge transport predicts universal power-law behavior in the current-voltage ($I$-$V$) characteristics for electrons tunneling into the edge. However, it has not been unambiguously observed in experiments in two-dimensional electron gases based on GaAs/GaAlAs heterostructures or quantum wells. One plausible cause is the fractional quantum Hall edge reconstruction, which introduces non-chiral edge modes. The coupling between counterpropagating edge modes can modify the exponent of the $I$-$V$ characteristics. By comparing the $\nu=1/3$ fractional quantum Hall states in modulation-doped semiconductor devices and in graphene devices, we show that the graphene-based systems have an experimental accessible parameter region to avoid the edge reconstruction, which is suitable for the exploration of the universal edge tunneling exponent predicted by the chiral Luttinger liquid theory.