Tension-induced non-linearities of flexural modes in nanomechanical resonators

TL;DR

This paper analyzes how tension-induced non-linearities affect the flexural modes of nanomechanical resonators, deriving their Hamiltonian up to fourth order and exploring their controllability via gate voltage for potential optomechanical applications.

Contribution

It derives the Hamiltonian of flexural modes including third and fourth order non-linearities and explores their control through gate voltage in large deformation regimes.

Findings

Third-order coupling can be non-zero due to dc deformation.

Fourth-order coupling is significant at low voltages.

Non-linearities can be detected via Duffing regime and mode coupling measurements.

Abstract

We consider the tension-induced non-linearities of mechanical resonators, and derive the Hamiltonian of the flexural modes up to the fourth order in the position operators. This tension can be controlled by a nearby gate voltage. We focus on systems which allow large deformations $u(x)\gg h$ compared to the thickness $h$ of the resonator and show that in this case the third-order coupling can become non-zero due to the induced dc deformation and offers the possibility to realize equations of motion encountered in optomechanics. The fourth-order coupling is relevant especially for relatively low voltages. It can be detected by accessing the Duffing regime, and by measuring frequency shifts due to mode-mode coupling.