Compressible Strips, Chiral Luttinger Liquids and All That Jazz

TL;DR

This paper reviews the physics of quantum Hall system edges, focusing on the relationship between macroscopic compressible strip models and microscopic chiral Luttinger liquid models, highlighting differences from ordinary 1D electron systems.

Contribution

It clarifies the connection between compressible strip models and chiral Luttinger liquids in quantum Hall edges, emphasizing their distinct origins of non-Fermi-liquid behavior.

Findings

Distinction between fractional quantum Hall edges and 1D electron gases.

Implications of compressible strip models for microscopic theories.

Insights into non-Fermi-liquid behavior in edge states.

Abstract

When the quantum Hall effect occurs in a two-dimensional electron gas, all low-energy elementary excitations are localized near the system edge. The edge acts in many ways like a one-dimensional ring of electrons, except that a finite current flows around the ring in equilibrium. This article is a brief and informal review of some of the physics of quantum Hall system edges. We discuss the implications of macroscopic {\em compressible strip} models for microscopic {chiral Luttinger liquid} models and make an important distinction between the origin of non-Fermi-liquid behavior in fractional quantum Hall edges and in usual one-dimensional electron gas systems.