Interaction of massless Dirac electrons with acoustic phonons in graphene at low temperatures

Abstract

Interaction of massless electrons with the acoustic phonons is studied in two-dimensional (2D) graphene at low temperatures by calculating phonon drag thermopower $S^g$ and hot-electron energy-loss rate $F\left(T\right)$. $S^g$ and $F\left(T\right)$ are studied as a function of temperature $T$ and electron concentration $n_s$. For very low temperatures $S^g\sim T^3$ and $F\left(T\right)\sim T^4$ in contrast to $S^g\sim T^4$ and $F\left(T\right)\sim T^5$ of unscreened deformation-potential coupling in usual 2D systems. We find that $S^g$ is related to the phonon limited mobility ${\mu }_p$ by $S^g$ ${\mu }_p=v_s\Lambda T^{-1}$ ($v_s$ is the phonon velocity and $\Lambda$ is the phonon mean-free path) validating Herring’s law for linear dispersion of electrons in graphene. In the low-temperature limit $S^g$, $F\left(T\right)\sim n_s^{-1/2}$. For comparison diffusion thermopower $S^d$ is calculated and $S^d\sim T$, $n_s^{-1/2}$. Our results are compared with those in the usual 2D systems.