Heat conduction in low-dimensional electron gases without and with a magnetic field

TL;DR

This study explores heat conduction in 2D electron gases with and without magnetic fields, revealing a dimensional crossover and the role of pseudomomentum conservation in heat transport behavior.

Contribution

It demonstrates that pseudomomentum conservation leads to normal heat conduction in magnetic fields, contrasting with anomalous behavior in similar low-dimensional systems.

Findings

Heat conductivity diverges as ln L at small sizes without magnetic field.

In the thermodynamic limit, heat conductivity scales as L^{1/3} without magnetic field.

Magnetic field induces finite, size-independent heat conductivity, indicating normal diffusion.

Abstract

We investigate the behavior of heat conduction in two-dimensional (2D) electron gases without and with a magnetic field. We perform simulations with the Multi-Particle-Collision approach, suitably adapted to account for the Lorenz force acting on the particles. For zero magnetic field, we find that the heat conductivity $\kappa$ diverges with the system size $L$ following the logarithmic relation $\kappa\thicksim \ln L$ (as predicted for two-dimensional (2D) systems) for small $L$ values; however, in the thermodynamic limit the heat conductivity tends to follow the relation $\kappa\thicksim L^{1/3}$, as predicted for one-dimensional (1D) fluids. This suggests the presence of a dimensional-crossover effect in heat conduction in electronic systems that adhere to standard momentum conservation. Under the magnetic field, time-reversal symmetry is broken and the standard momentum conservation in the system is no longer satisfied but the \emph{pseudomomentum} of the system is still conserved. In contrast with the zero-field case, both equilibrium and non-equilibrium simulations indicate a finite heat conductivity independent on the system size $L$ as $L$ increases. This indicates that pseudomomentum conservation can exhibit normal diffusive heat transport, which differs from the abnormal behavior observed in low-dimensional coupled charged harmonic oscillators with pseudomomentum conservation in a magnetic field. These findings support the validity of the hydrodynamic theory in electron gases and clarify that pseudomomentum conservation is not enough to ensure the anomalous behavior of heat conduction.