Quantum Hall Effects at Finite Temperatures

TL;DR

This paper investigates how finite temperature affects the integer and fractional quantum Hall effects within the composite fermion model, revealing loss of universality and quantization at non-zero temperatures, while aligning with experimental observations.

Contribution

It provides a detailed analysis of finite temperature effects on quantum Hall states using the composite fermion model, highlighting the need for refinement in microscopic property descriptions.

Findings

Universality and quantization are lost at finite temperatures.

The model aligns with bulk FQHE results but needs refinement for microscopic details.

Threshold temperatures for observing FQHE states are qualitatively explained.

Abstract

We study the finite temperature (FT) effects on integer quantum Hall effect (IQHE) and fractional quantum Hall effect (FQHE) as predicted by the composite fermion model. We find that at $T\neq 0$, universality is lost, as is quantization because of a new scale $T_0=\pi\rho /m^\ast p$. We find that this loss is not inconsistent with the experimentally observed accuracies. While the model seems to work very well for IQHE, it agrees with the bulk results of FQHE but is shown to require refinement in its account of microscopic properties such as the effective mass. Our analysis also gives a qualitative account of the threshold temperatures at which the FQHE states are seen experimentally. Finally, we extract model independent features of quantum Hall effect at FT, common to all Chern-Simons theories that employ mean field ansatz.