Deviation from the normal mode expansion in a coupled graphene-nanomechanical system

A significant deviation from the normal mode expansion is observed in the optomechanically measured thermal noise of a graphene membrane suspended on a silicon nitride nanoresonator. This deviation is due to the heterogeneous character of mechanical dissipation over the spatial extent of coupled eigenmodes, which is tuned through an avoided anticrossing. We demonstrate that the fluctuation-dissipation theorem permits a proper evaluation of the thermal noise of the coupled nanomechanical system. Since a good spatial homogeneity is delicate to ensure at the nanoscale, this approach is fundamental to correctly describing the thermal noise of nanomechanical systems which ultimately impact their sensing capacity.