Controlling electron-phonon interactions in graphene at ultra high carrier densities

We report on the temperature dependent electron transport in graphene at different carrier densities $n$. Employing an electrolytic gate, we demonstrate that $n$ can be adjusted up to 4$\times10^{14}$cm$^{-2}$ for both electrons and holes. The measured sample resistivity $\rho$ increases linearly with temperature $T$ in the high temperature limit, indicating that a quasi-classical phonon distribution is responsible for the electron scattering. As $T$ decreases, the resistivity decreases more rapidly following $\rho (T) \sim T^{4}$. This low temperature behavior can be described by a Bloch-Gr\"{u}neisen model taking into account the quantum distribution of the 2-dimensional acoustic phonons in graphene. We map out the density dependence of the characteristic temperature $\Theta_{BG}$ defining the cross-over between the two distinct regimes, and show, that for all $n$, $\rho(T)$ scales as a universal function of the normalized temperature $T/\Theta_{BG}$.