# The Effect of Disorder on Local Electron Temperature in Quantum Hall Systems

## TL;DR

This study models how disorder affects local electron temperature in quantum Hall systems, revealing antisymmetric temperature variations linked to incompressible strips and impurity levels, using thermal-hydrodynamical equations.

## Contribution

It introduces a detailed calculation of local electron temperature considering disorder effects in quantum Hall systems, highlighting the impact of impurities and sample width.

## Key findings

- Electron temperature varies antisymmetrically across the sample.
- Disorder and impurity levels significantly influence local temperature.
- Temperature distribution correlates with incompressible strip locations.

## Abstract

The local electron temperature distribution is calculated considering a two dimensional electron system in the integer quantum Hall regime in presence of disorder and uniform perpendicular magnetic fields. We solve thermal-hydrodynamical equations to obtain the spatial distribution of the local electron temperature in the linear-response regime. It is observed that, the variations of electron temperature exhibit an antisymmetry regarding the center of the sample in accordance with the location of incompressible strips. To understand the effect of sample mobility on the local electron temperature we impose a disorder potential calculated within the screening theory. Here, long range potential fluctuations are assumed to simulate cumulative disorder potential depending on the impurity atoms. We observe that the local electron temperature strongly depends on the number of impurities in narrow samples.