Acoustic phonon scattering limited carrier mobility in two-dimensional 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) two-dimensional graphene layers as a function of temperature $(T)$ and carrier density $(n)$. We find a temperature-dependent phonon-limited resistivity ρₚₕ(T) to be linear in temperature for T500.3em0exK with the room-temperature intrinsic mobility reaching the values of above 10⁵0.3em0excm²∕V0.2em0exs. We comment on the low-temperature Bloch--Gr\"uneisen behavior where ρₚₕ(T)~T⁴ for unscreened electron-phonon coupling.