Out of plane vibrations are suppressed in graphene layers placed on a substrate. These vibrations, in suspended samples, are relevant for the understanding of properties such as the electrical resistivity, the thermal expansion coefficient, and others. We use a general framework to study the properties of the out of plane mode in graphene on different substrates, taking into account the dynamics of the substrate. We discuss broadening of this mode and how it hybridizes with the substrate Rayleigh mode, comparing our model with experimental observations. We use the model to estimate the substrate induced changes in the thermal expansion coefficient and in the temperature dependence of the electrical resistivity.

• Received 24 April 2013

DOI:https://doi.org/10.1103/PhysRevB.88.115418