Flexural mode of graphene on a substrate

TL;DR

This paper develops a theoretical framework to analyze out-of-plane vibrational modes in graphene on substrates, exploring how substrate interactions influence properties like thermal expansion and resistivity.

Contribution

It introduces a general model for studying out-of-plane modes in supported graphene and applies it to predict substrate effects on physical properties.

Findings

Substrate interactions modify graphene's out-of-plane vibrational modes.

The model estimates changes in thermal expansion coefficient due to substrate.

Predictions include substrate-induced variations in resistivity with temperature.

Abstract

Out of plane vibrations are suppressed in graphene layers placed on a substrate. These modes, in suspended samples, are relevant for the understanding of properties such as the resistivity, the thermal expansion coefficient, and other. We present a general framework for the study of the properties of out of plane modes in graphene on different substrates. We use the model to estimate the substrate induced changes in the thermal expansion coefficient, or in the temperature dependence of the resistivity.