The unique properties and atomic thickness of two-dimensional (2D) materials enable smaller and better nanoelectromechanical sensors with novel functionalities. During the last decade, many studies have successfully shown the feasibility of using suspended membranes of 2D materials in pressure sensors, microphones, accelerometers, and mass and gas sensors. In this review, we explain the different sensing concepts and give an overview of the relevant material properties, fabrication routes, and device operation principles. Finally, we discuss sensor readout and integration methods and provide comparisons against the state of the art to show both the challenges and promises of 2D material-based nanoelectromechanical sensing.

The dynamics of suspended two-dimensional (2D) materials has received increasing attention during the last decade, yielding new techniques to study and interpret the physics that governs the motion of atomically thin layers. This has led to insights into the role of thermodynamic and nonlinear effects as well as the mechanisms that govern dissipation and stiffness in these resonators. In this review, we present the current state-of-the-art in the experimental study of the dynamics of 2D membranes. The focus will be both on the experimental measurement techniques and on the interpretation of the physical phenomena exhibited by atomically thin membranes in the linear and nonlinear regimes. We will show that resonant 2D membranes have emerged both as sensitive probes of condensed matter physics in ultrathin layers, and as sensitive elements to monitor small external forces or other changes in the environment. New directions for utilizing suspended 2D membranes for material characterization, thermal transport, and gas interactions will be discussed and we conclude by outlining the challenges and opportunities in this upcoming field.

Stochastic switching between the two bistable states of a strongly driven mechanical resonator enables detection of weak signals based on probability distributions, in a manner that mimics biological systems. However, conventional silicon resonators at the microscale require a large amount of fluctuation power to achieve a switching rate in the order of a few Hertz. Here, we employ graphene membrane resonators of atomic thickness to achieve a stochastic switching rate of 4.1 kHz, which is 100 times faster than current state-of-the-art. The (effective) temperature of the fluctuations is approximately 400 K, which is 3000 times lower than the state-of-the-art. This shows that these membranes are potentially useful to transduce weak signals in the audible frequency domain. Furthermore, we perform numerical simulations to understand the transition dynamics of the resonator and use analytical expressions to investigate the relevant scaling parameters that allow high-frequency, low-temperature stochastic switching to be achieved in mechanical resonators.

The thermal response of graphene is expected to be extremely fast due to its low heat capacity and high thermal conductivity. In this work, the thermal response of suspended single-layer graphene membranes is investigated by characterization of their mechanical motion in response to a high-frequency modulated laser. A characteristic delay time $\tau$ between the optical intensity and mechanical motion is observed, which is attributed to the time required to raise the temperature of the membrane. We find, however, that the measured time constants are significantly larger than the predicted ones based on values of the specific heat and thermal conductivity. In order to explain the discrepancy between measured and modeled $\tau$, a model is proposed that takes a thermal boundary resistance at the edge of the graphene drum into account. The measurements provide a noninvasive way to characterize thermal properties of suspended atomically thin membranes, providing information that can be hard to obtain by other means.

In the field of nanomechanics, parametric excitations are of interest since they can greatly enhance sensing capabilities and eliminate cross-talk. Above a certain threshold of the parametric pump, the mechanical resonator can be brought into parametric resonance. Here we demonstrate parametric resonance of suspended single-layer graphene membranes by an efficient opto-thermal drive that modulates the intrinsic spring constant. With a large amplitude of the optical drive, a record number of 14 mechanical modes can be brought into parametric resonance by modulating a single parameter: the pre-tension. A detailed analysis of the parametric resonance allows us to study nonlinear dynamics and the loss tangent of graphene resonators. It is found that nonlinear damping, of the van der Pol type, is essential to describe the high amplitude parametric resonance response in atomically thin membranes.