Dirac Materials and an Identity for the Grand Potential of the Nondegenerate Statistical Thermodynamic Regime

Abstract

We examine the question “Can Dirac materials exist in a nondegenerate statistical state?,” deriving and employing an identity for the thermodynamic Grand Potential $\Omega$ (per unit volume/area) in the low density nondegenerate statistical regime, relating it to the density $n$ as $\Omega = -\beta ^{-1} n$ ( $\beta ^{-1} = \kappa _{B} T$ is thermal energy, $\kappa _{B}$ is the Boltzmann constant, and $T$ is Kelvin temperature). The implications of this identity for Dirac materials are explored. The identity is universally valid for all thermodynamic systems in equilibrium in the nondegenerate, low density statistical regime, irrespective of size, dimensionality or applied static fields. Phenomena that may contribute to the realization of such a nondegenerate statistical equilibrium state in Dirac materials are discussed.