Scaling Approach to the Phase Diagram of Quantum Hall Systems

TL;DR

This paper introduces a scaling-based classification of liquid and solid phases in quantum Hall systems at non-integer fillings, providing a criterion for mean-field validity and aligning well with experimental data.

Contribution

It offers a novel classification scheme and a mean-field validity criterion for quantum Hall phases using scaling arguments on effective interactions.

Findings

Classification scheme matches experimental observations

Mean-field approximation validity criterion established

Finite-temperature effects are successfully modeled

Abstract

We present a simple classification of the different liquid and solid phases of quantum Hall systems in the limit where the Coulomb interaction between the electrons is significant, i.e. away from integral filling factors. This classification, and a criterion for the validity of the mean-field approximation in the charge-density-wave phase, is based on scaling arguments concerning the effective interaction potential of electrons restricted to an arbitrary Landau level. Finite-temperature effects are investigated within the same formalism, and a good agreement with recent experiments is obtained.