Electron-hole collision-limited resistance of gapped graphene

Collisions between electrons and holes can dominate the carrier scattering in clean graphene samples in the vicinity of charge neutrality point. While electron-hole limited resistance in pristine gapless graphene is well-studied, its evolution with induction of band gap $E_g$ is less explored. Here, we derive the functional dependence of electron-hole limited resistance of gapped graphene ${\rho }_{eh}$ on the ratio of gap and thermal energy $E_g\mathrm{/}kT$. At low temperatures and large band gaps, the resistance grows linearly with $E_g\mathrm{/}kT$, and possesses a minimum at $E_g\approx 2.5kT$. This contrast to the Arrhenius activation-type behaviour for intrinsic semiconductors. Introduction of impurities restores the Arrhenius law for resistivity at low temperatures and/or high doping densities. The hallmark of electron-hole collision effects in graphene resistivity at charge neutrality is the crossover between exponential and power-law resistivity scalings with temperature.