Integer Quantum Hall Effect: Disorder, temperature, floating, and plateau width

TL;DR

This paper provides a comprehensive theoretical analysis of how disorder and temperature influence the integer quantum Hall effect, addressing key experimental questions about plateau width, conductance behavior, and phase transitions.

Contribution

It offers new insights into the combined effects of disorder and temperature on IQHE, highlighting their intricate interplay and impact on plateau width and conductance scaling.

Findings

Disorder and temperature nonmonotonically affect IQHE plateau width.

Disorder and temperature are intrinsically connected in IQHE behavior.

The study suggests potential experimental directions based on the interplay of disorder and temperature.

Abstract

We theoretically consider disorder and temperature effects on the integer quantum Hall effect (IQHE) using a variety of distinct and complementary analytical and numerical techniques. In particular, we address simple, physical, and experimentally relevant questions: How does disorder and/or temperature affect the IQHE plateau width? Does the plateau width increase or decrease with disorder and/or temperature? What happens to the peak in the longitudinal conductance with increasing disorder/temperature? Does the longitudinal conductance obey any universal scaling property? Is there "floating" with increasing disorder and/or decreasing magnetic field? Can disorder destroy the IQHE? Is there an IQHE to localization transition? What is the Landau level dependence of the plateau width? Our detailed theory provides answers to these and other related experimentally relevant questions. We discuss our results in the context of existing experimental results and suggest future experiments arising from our work. A key finding is that disorder and temperature are intrinsically connected in affecting IQHE, and there is an intricate interplay between them leading to nonmonotonicity in how the IQHE plateau width behaves as a function of increasing disorder. Both must be considered on an equal footing in understanding IQHE experiments.