Acoustic phonon scattering limited carrier mobility in 2D extrinsic graphene

We theoretically calculate the phonon scattering limited electron mobility in extrinsic (i.e. gated or doped with a tunable and finite carrier density) 2D graphene layers as a function of temperature $(T)$ and carrier density $(n)$. We find a temperature dependent phonon-limited resistivity $\rho_{ph}(T)$ to be linear in temperature for $T\agt 50 K$ with the room temperature intrinsic mobility reaching values above $10^5$ cm$^2/Vs$. We comment on the low-temperature Bloch-Gr\"{u}neisen behavior where $\rho_{ph}(T) \sim T^4$ for unscreened electron-phonon coupling.