First-principles analysis of electron-phonon interactions in graphene

The electron-phonon interaction in monolayer graphene is investigated using density-functional perturbation theory. The results indicate that the electron-phonon interaction strength is of comparable magnitude for all four in-plane phonon branches and must be considered simultaneously. Moreover, the calculated scattering rates suggest an acoustic-phonon contribution that is much weaker than previously thought, revealing an important role of optical phonons even at low energies. Accordingly it is predicted, in good agreement with a recent measurement, that the intrinsic mobility of graphene may be more than an order of magnitude larger than the already high values reported in suspended samples.

Figure 1

(Color online) Electron-phonon interaction matrix elements $\left|g_{\mathbf{k}+\mathbf{q},\mathbf{k}}^{\left(i,j\right)\nu }\right|$ (in units of eV) calculated by DFPT for $\mathbf{k}$ at the conduction-band minimum (i.e., the Dirac point) as a function of phonon wave vector $\mathbf{q}$. High anisotropy beyond the long-wavelength approximation is clearly visible. The presence of Kohn anomalies reported earlier is revealed as the peaks (light color) at three equivalent Dirac points for TO and at the center of the Brillouin zone for LO.

Figure 2

(Color online) Phonon (a) emission and (b) absorption scattering rates at $T=300\text{K}$ as functions of electron energy $E_{\mathbf{k}}$, as $\mathbf{k}$ changes along the $K\text{−}\Gamma$ direction in monolayer graphene. The contributions of all six branches are shown separately. The out-of-plane phonons (ZA and ZO) do not play an important role. At very low electron energies $\left(E<k_{B}T\right)$, the scattering with absorption of TO phonons is dominant.

Figure 3

(Color online) Intrinsic resistivity as a function of temperature. At $T<200\text{K}$, the quasielastic intravalley scattering with in-plane acoustic phonons is dominant (dashed line). At higher temperatures, the contributions of both optical phonons and intervalley scattering by TA and LA modes (dashed-dotted line) lead to an exponential growth of the resistivity. The inset shows the low-field mobilities at $T=50$ and 300 K, as determined from the slope of the drift-velocity versus electric field characteristic obtained by a full-band Monte Carlo simulation.

Figure 4

(Color online) Total scattering rate as a function of electron energy at $T=300\text{K}$. The dotted line shows the fitted curve calculated from Eq. (5). Clearly, the role of optical-phonon scattering and intervalley transfer must be taken into account in most cases judging from the discrepancy between the solid (total) and dashed (TA and LA intravalley) lines.