Thermohydrodynamics in Quantum Hall Systems

TL;DR

This paper develops a comprehensive thermohydrodynamic theory for two-dimensional electron systems in quantum Hall regimes, incorporating nonlinear transport and local equilibrium, to explain phenomena like the Ettingshausen effect.

Contribution

It introduces a novel model of flux densities based on hopping and drift processes in a slowly varying random potential, extending thermohydrodynamics to quantum Hall systems.

Findings

Derived flux expressions for standard transport experiments.

Formulated conservation equations in terms of transport flux components.

Applied theory to explain the Ettingshausen effect with temperature gradients.

Abstract

A theory of thermohydrodynamics in two-dimensional electron systems in quantizing magnetic fields is developed including a nonlinear transport regime. Spatio-temporal variations of the electron temperature and the chemical potential in the local equilibrium are described by the equations of conservation with the number and thermal-energy flux densities. A model of these flux densities due to hopping and drift processes is introduced for a random potential varying slowly compared to both the magnetic length and the phase coherence length. The flux measured in the standard transport experiment is derived and is used to define a transport component of the flux density. The equations of conservation can be written in terms of the transport component only. As an illustration, the theory is applied to the Ettingshausen effect, in which a one-dimensional spatial variation of the electron temperature is produced perpendicular to the current.