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 $T\text{agt}50K$ with the room temperature intrinsic mobility reaching values above ${10}^5$ cm${}^2\mathrm{/}Vs$. We comment on the low-temperature Bloch-Gr"{u}neisen behavior where ${\rho }_{ph}(T)\sim T^4$ for unscreened electron-phonon coupling.