High-temperature behavior of supported graphene: Electron-phonon coupling and substrate-induced doping

The temperature-dependent electronic structure and electron-phonon coupling of weakly doped supported graphene is studied by angle-resolved photoemission spectroscopy and ab initio molecular dynamics simulations. The electron-phonon coupling is found to be extremely weak, reaching the lowest value ever reported for any material. However, the temperature-dependent dynamic interaction with the substrate leads to a complex and dramatic change in the carrier density and type in graphene. These changes in the electronic structure are mainly caused by fluctuations in the graphene-substrate distance.

Figure 1

Electronic structure of graphene on Ir(111) determined by ARPES. (a)–(c) Spectra taken through the $\overline{K}$ point of the Brillouin zone perpendicular to the $\overline{\Gamma }$-$\overline{K}$ direction [dashed line in the inset of (a)] for three different temperatures. $k_{\parallel }$ is measured relative to the Dirac point. (d) Imaginary part of the self-energy below the Dirac point obtained from the MDC linewidth. The solid line is a result of fitting Eq. (1) to the data using the given parameters. (e) ${\chi }^2$ value for the fit in (d) as a function of the Debye temperature ${\theta }_D$ and the electron-phonon coupling strength $\lambda$. (f) Dirac point energy as a function of temperature, estimated from the extrapolated high binding energy dispersion.

Figure 2

Electronic and geometric structure of suspended and supported graphene determined by ab initio molecular dynamics. (a) DOS (from $p$ electrons) of freely suspended graphene. (b) DOS for freely suspended graphene in the vicinity of the Fermi energy for two temperatures. The solid line is the DOS calculated from the analytic, linear dispersion. (c) Average distance between the Ir(111) surface and graphene during 60 ps simulations at 300 and 1000 K. The inset shows the geometry of the system after 45 ps at 1000 K. (d) and (e) Snapshots of the projected DOS on the carbon atoms at 30 and 45 ps, corresponding to configurations with similar and different graphene-Ir distances for the two temperatures, respectively. The solid lines have the same shape as in (b) but merely serve as a guide to the eye here.