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 multiparticle collision approach, suitably adapted to account for the Lorenz force acting on the particles. For zero magnetic field, we find that the heat conductivity κ diverges with the system size L following the logarithmic relation κ∼lnL (as predicted for 2D systems) for small L values; however, in the thermodynamic limit the heat conductivity tends to follow the relation κ∼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 pseudomomentum of the system is still conserved. In contrast with the zero-field case, both equilibrium and nonequilibrium 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.