Nanomechanical vibrational response from electrical mixing measurements

TL;DR

This paper introduces a reliable method to isolate and measure the true mechanical vibrations of nanomechanical resonators using electrical mixing, improving accuracy in spectral and quadrature measurements and enabling effective mass calibration.

Contribution

The authors present a novel technique to separate mechanical signals from electrical background in nanomechanical resonators, enhancing measurement precision and enabling direct mass determination.

Findings

Successful extraction of pure mechanical vibrations

Calibration of signals into displacement units

Direct measurement of effective mass

Abstract

Driven nanomechanical resonators based on low-dimensional materials are routinely and efficiently detected with electrical mixing measurements. However, the measured signal is a non-trivial combination of the mechanical eigenmode displacement and an electrical contribution, which makes the extraction of the driven mechanical response challenging. Here, we report a simple yet reliable method to extract solely the driven mechanical vibrations by eliminating the contribution of pure electrical origin. This enables us to measure the spectral mechanical response as well as the driven quadratures of motion. We further show how to calibrate the measured signal into units of displacement. Additionally, we utilize the pure electrical contribution to directly determine the effective mass of the measured mechanical mode. Our method marks a key step forward in the study of nanoelectromechanical resonators based on low-dimensional materials in both the linear and the nonlinear regime.