Coulomb Drag in Graphene

We study the Coulomb drag between two single graphene sheets in intrinsic and extrinsic graphene systems with no interlayer tunneling. The general expression for the nonlinear susceptibility appropriate for single-layer graphene systems is derived using the diagrammatic perturbation theory, and the corresponding exact zero-temperature expression is obtained analytically. We find that, despite the existence of a non-zero conductivity in an intrinsic graphene layer, the Coulomb drag between intrinsic graphene layers vanishes at all temperatures. In extrinsic systems, we obtain numerical results and an approximate analytical result for the drag resistivity $\rho_{\textrm{D}}$, and find that $\rho_{\textrm{D}}$ goes as $T^2$ at low temperature $T$, as $1/d^4$ for large bilayer separation $d$ and $1/n^3$ for high carrier density $n$. We also discuss qualitatively the effect of plasmon-induced enhancement on the Coulomb drag, which should occur at a temperature of the order of or higher than the Fermi temperature.