Theoretical Investigation of Local Electron Temperature in Quantum Hall Systems

TL;DR

This paper develops a theoretical model to analyze the spatial distribution of local electron temperature in quantum Hall systems, considering electrostatic potentials and current-induced temperature variations.

Contribution

It introduces a self-consistent thermo-hydrodynamical approach to calculate local electron temperature in quantum Hall regimes under external current.

Findings

Electron temperature depends on compressible and incompressible strip formation

The model predicts temperature variations in response to external currents

The approach links electrostatic potentials with thermal behavior in quantum Hall systems

Abstract

In this work we solve thermo-hydrodynamical equations considering a two dimensional electron system in the integer quantum Hall regime, to calculate the spatial distribution of the local electron temperature. We start from the self-consistently calculated electrostatic and electrochemical potentials in equilibrium. Next, by imposing an external current, we investigate the variations of the electron temperature in the linear-response regime. Here a local relation between the electron density and conductivity tensor elements is assumed. Following the Ohm's law we obtain local current densities and by implementing the results of the thermo-hydrodynamical theory, calculate the local electron temperature. We observe that the local electron temperature strongly depends on the formation of compressible and incompressible strips.