Charge transport in gapless electron-hole systems with arbitrary band dispersion

Abstract

Using the semiclassical Boltzmann transport theory, we analytically consider dc charge transport in gapless electron-hole (both chiral and nonchiral) systems in the presence of resistive scattering due to static disorder arising from random quenched impurities in the background. We obtain the dependence of the Boltzmann conductivity on carrier density and temperature for arbitrary band dispersion in arbitrary dimensionality assuming long-range $(\ensuremath{\sim}1/r)$ Coulomb disorder and zero-range white-noise disorder $[\ensuremath{\sim}\ensuremath{\delta}(r)]$. We establish that the temperature and the density dependence of the Boltzmann conductivity manifests scaling behaviors determining, respectively, the intrinsic semimetallic or the extrinsic metallic property of the gapless system. Our results apply equally well to both chiral and nonchiral gapless systems, and provide a qualitative understanding of the dependence of the Boltzmann conductivity on the band dispersion in arbitrary dimensionality.