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

TL;DR

This study investigates deviations from the normal mode expansion in a graphene-silicon nitride nanomechanical system, revealing the importance of local dissipation effects on thermal noise and sensing accuracy.

Contribution

It demonstrates that heterogeneous dissipation causes deviations from normal mode expansion, and shows that local susceptibility measurements can still validate the fluctuation-dissipation theorem.

Findings

Deviation from normal mode expansion observed

Local mechanical susceptibility measurement confirms fluctuation-dissipation theorem

Implications for accurate thermal noise modeling in nanomechanical sensors

Abstract

We optomechanically measure the vibrations of a nanomechanical system made of a graphene membrane suspended on a silicon nitride nanoresonator. When probing the thermal noise of the coupled nanomechanical device, we observe a significant deviation from the normal mode expansion. It originates from the heterogeneous character of mechanical dissipation over the spatial extension of coupled eigenmodes, which violates one of the fundamental prerequisite for employing this commonly used description of the nanoresonators' thermal noise. We subsequently measure the local mechanical susceptibility and demonstrate that the fluctuation-dissipation theorem still holds and permits a proper evaluation of the thermal noise of the nanomechanical system. Since it naturally becomes delicate to ensure a good spatial homogeneity at the nanoscale, this approach is fundamental to correctly describe the thermal noise of nanomechanical systems which ultimately impact their sensing capacity.