  One of the salient features of graphene is the very high carrier mobility
that implies tremendous potential for use in electronic devices. Unfortunately,
transport measurements find the expected high mobility only in freely suspended
graphen. When supported on a surface, graphene shows a strongly reduced
mobility, and an especially severe reduction for temperatures above 200 K. A
temperature-dependent mobility reduction could be explained by scattering of
carriers with phonons, but this is expected to be weak for pristine,
weakly-doped graphene. The mobility reduction has therefore been ascribed to
the interaction with confined ripples or substrate phonons. Here we study the
temperature-dependent electronic structure of supported graphene by
angle-resolved photoemission spectroscopy, a technique that can reveal the
origin of the phenomena observed in transport measurements. We show that the
electron-phonon coupling for weakly-doped, supported graphene on a metal
surface is indeed 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 type and
density that is relevant for transport. Using ab initio molecular dynamics
simulations, we show that these changes in the electronic structure are mainly
caused by fluctuations in the graphene-substrate distance.
