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

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.