Kohn Anomalies and Electron-Phonon Interactions in Graphite

We demonstrate that graphite phonon dispersions have two Kohn anomalies at the $\Gamma \mathrm{\text{−}}{E}_{2g}$ and $\mathbf{K}\mathrm{\text{−}}{A}_1^{\prime }$ modes. The anomalies are revealed by two sharp kinks. By an exact analytic derivation, we show that the slope of these kinks is proportional to the square of the electron-phonon coupling (EPC). Thus, we can directly measure the EPC from the experimental dispersions. The $\Gamma \mathrm{\text{−}}{E}_{2g}$ and $\mathbf{K}\mathrm{\text{−}}{A}_1^{\prime }$ EPCs are particularly large, while they are negligible for all the other modes at $\Gamma$ and $\mathbf{K}$.

Figure 1

Upper panel: lines: phonon dispersion of graphene (GE), calculated at the experimental and equilibrium lattice spacings ($a_{\exp }$ and $a_{\mathrm{t}\mathrm{h}}$). Points: experimental data from Ref. 9. The red straight lines at $\Gamma$ and $\mathbf{K}$ are obtained from Eqs. (8, 10). The two lower panels correspond to the dotted windows in the upper panel. The points are theoretical frequencies obtained by direct calculation. A single graphene band corresponds to two almost degenerate graphite (GI) bands.

Figure 2

Graphene HOB around $\Gamma$ and $\mathbf{K}$ as a function of smearing. Points are calculated frequencies for $a_{\mathrm{t}\mathrm{h}}$. Lines are guides to the eye. The red straight lines plot Eqs. (8, 10).