Interplay between Raman shift and thermal expansion in graphene: temperature-dependent measurements and analysis of substrate corrections

Measurements and calculations have shown significant disagreement regarding the sign and variations of the thermal expansion coefficient (TEC) of graphene $alpha(T)$. Here we report dedicated Raman scattering experiments conducted for graphene monolayers deposited on silicon nitride substrates and over the broad temperature range 150--900~K. The relation between those measurements for the G band and the graphene TEC, which involves correcting the measured signal for the mismatch contribution of the substrate, is analyzed based on various theoretical candidates for $alpha(T)$. Contrary to calculations in the quasiharmonic approximation, a many-body potential reparametrized for graphene correctly reproduces experimental data. These results indicate that the TEC is more likely to be positive above room temperature.