Quantum Hall Effect in Quasi-One-Dimensional Conductors: The Roles of Moving FISDW, Finite Temperature, and Edge States

TL;DR

This paper reviews the theory of the quantum Hall effect in quasi-one-dimensional conductors with FISDW, highlighting the roles of moving FISDW, temperature, and edge states, and providing simple derivations and physical insights.

Contribution

It offers a new, accessible derivation of the QHE in FISDW states, emphasizing the physical interpretation and effects of FISDW motion and temperature dependence.

Findings

Hall conductivity depends on temperature similarly to Fröhlich current

Moving FISDW cancels the Hall effect in the free state

Edge states provide a transparent derivation of QHE in FISDW

Abstract

This paper reviews recent developments in the theory of the quantum Hall effect (QHE) in the magnetic-field-induced spin-density-wave (FISDW) state of the quasi-one-dimensional organic conductors (TMTSF)$_2$X. The origin and the basic features of the FISDW are reviewed. The QHE in the pinned FISDW state is derived in several simple, transparent ways, including the edge states formulation of the problem. The temperature dependence of the Hall conductivity is found to be the same as the temperature dependence of the Fr\"ohlich current. It is shown that, when the FISDW is free to move, it produces an additional contribution to the Hall conductivity that nullifies the total Hall effect. The paper is written on mathematically simple level, emphasizes physical meaning over sophisticated mathematical technique, and uses inductive, rather than deductive, reasoning.