Chirality-dependent phonon-limited resistivity in multiple layers of graphene

Abstract

We develop a theory for the temperature and density dependence of phonon-limited resistivity $\rho(T)$ in bilayer and multilayer graphene, and compare with the corresponding monolayer result. For the unscreened case, we find $\rho \approx C T$ with $C \propto v_{\rm F}^{-2}$ in the high-temperature limit, and $\rho \approx A T^4$ with $A \propto v_{\rm F}^{-2} k_{\rm F}^{-3}$ in the low-temperature Bloch-Gr\"uneisen limit, where $v_{\rm F}$ and $k_{\rm F}$ are Fermi velocity and Fermi wavevector, respectively. If screening effects are taken into account, $\rho \approx C T$ in the high-temperature limit with a renormalized $C$ which is a function of the screening length, and $\rho \approx A T^6$ in the low-temperature limit with $A \propto k_{\rm F}^{-5}$ but independent of $v_{\rm F}$. These relations hold in general with $v_{\rm F}$ and a chiral factor in $C$ determined by the specific chiral band structure for a given density.