Hydrodynamic equations for an electron gas in graphene

TL;DR

This paper reviews and extends hydrodynamic equations for electron gases, especially in graphene, using maximum entropy closure, and explores various asymptotic regimes for electrons on graphene sheets.

Contribution

It introduces non-isothermal hydrodynamic equations for electrons in graphene considering spin-orbit interaction and Fermi-Dirac statistics, extending previous models.

Findings

Extended hydrodynamic models to non-isothermal conditions.

Analyzed asymptotic regimes of electron behavior in graphene.

Applied maximum entropy closure to spin-orbit coupled electrons.

Abstract

In this paper we review, and extend to the non-isothermal case, some results concerning the application of the maximum entropy closure technique to the derivation of hydrodynamic equations for particles with spin-orbit interaction and Fermi-Dirac statistics. In the second part of the paper we treat in more details the case of electrons on a graphene sheet and investigate various asymptotic regimes.