  Nanomechanical spectroscopy (NMS) is a recently developed approach to
determine optical absorption spectra of nanoscale materials via mechanical
measurements. It is based on measuring changes in the resonance frequency of a
membrane resonator vs. the photon energy of incoming light. This method is a
direct measurement of absorption, which has practical advantages compared to
common optical spectroscopy approaches. In the case of two-dimensional (2D)
materials, NMS overcomes limitations inherent to conventional optical methods,
such as the complications associated with measurements at high magnetic fields
and low temperatures. In this work, we develop a protocol for NMS of 2D
materials that yields two orders of magnitude improved sensitivity compared to
previous approaches, while being simpler to use. To this end, we use electrical
sample actuation, which simplifies the experiment and provides a reliable
calibration for greater accuracy. Additionally, the use of low-stress silicon
nitride membranes as our substrate reduces the noise-equivalent power to $NEP =
890 fW/\sqrt{Hz}$, comparable to commercial semiconductor photodetectors. We
use our approach to spectroscopically characterize a two-dimensional transition
metal dichalcogenide (WS$_2$), a layered magnetic semiconductor (CrPS$_4$), and
a plasmonic supercrystal consisting of gold nanoparticles.
