Coulomb drag in graphene near the Dirac point

We study Coulomb drag in double-layer graphene near the Dirac point. A particular emphasis is put on the case of clean graphene, with transport properties dominated by the electron-electron interaction. Using the quantum kinetic equation framework, we show that the drag becomes $T$-independent in the clean limit, $T\tau \to \infty$, where $T$ is temperature and $1/\tau$ impurity scattering rate. For stronger disorder (or lower temperature), $T\tau \ll 1/\alpha^2$, where $\alpha$ is the interaction strength, the kinetic equation agrees with the leading-order ($\alpha^2$) perturbative result. At still lower temperatures, $T\tau \ll 1$ (diffusive regime) this contribution gets suppressed, while the next-order ($\alpha^3$) contribution becomes important; it yields a peak centered at the Dirac point with a magnitude that grows with lowering $T\tau$.