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.

Coupled nanomechanical resonators made of two-dimensional materials are promising for processing information with mechanical modes. However, the challenge for these systems is to control the coupling. Here, we demonstrate strong coupling of motion between two suspended membranes of the magnetic 2D material FePS3. We describe a tunable electromechanical mechanism for control over both the resonance frequency and the coupling strength using a gate voltage electrode under each membrane. We show that the coupling can be utilized for transferring data between drums by amplitude modulation. Finally, we also study the temperature dependence of the coupling and how it is affected by the antiferromagnetic phase transition characteristic of this material. The presented electrical coupling of resonant magnetic 2D membranes holds the promise of transferring mechanical energy over a distance at low electrical power, thus enabling novel data readout and information processing technologies.

The high flexibility, impermeability and strength of graphene membranes are key properties that can enable the next generation of nanomechanical sensors. However, for capacitive pressure sensors, the sensitivity offered by a single suspended graphene membrane is too small to compete with commercial sensors. Here, we realize highly sensitive capacitive pressure sensors consisting of arrays of nearly ten thousand small, freestanding double-layer graphene membranes. We fabricate large arrays of small-diameter membranes using a procedure that maintains the superior material and mechanical properties of graphene, even after high-temperature annealing. These sensors are readout using a low-cost battery-powered circuit board, with a responsivity of up to 47.8 aF Pa⁻¹ mm⁻², thereby outperforming the commercial sensors.

Complex oxide thin films and heterostructures exhibit a variety of electronic phases, often controlled by the mechanical coupling between film and substrate. Recently it has become possible to isolate epitaxially grown single-crystalline layers of these materials, enabling the study of their properties in the absence of interface effects. In this work, we use this technique to create nanomechanical resonators made out of SrTiO₃ and SrRuO₃. Using laser interferometry, we successfully actuate and measure the motion of the nanodrum resonators. By measuring the temperature-dependent mechanical response of the SrTiO₃ resonators, we observe signatures of a structural phase transition, which affects both the strain and mechanical dissipation in the resonators. Here, we demonstrate the feasibility of integrating ultrathin complex oxide membranes for realizing nanoelectromechanical systems on arbitrary substrates and present a novel method of detecting structural phase transitions in these exotic materials.

Despite theoretical predictions that graphene should be impermeable to all gases, practical experiments on sealed graphene nanodrums show small leak rates. Thus far, the exact mechanism for this permeation has remained unclear, because different potential leakage pathways have not been studied separately. Here, we demonstrate a sealing method that consists of depositing SiO₂ across the edge of suspended multilayer graphene flakes using electron beam-induced deposition. By sealing, leakage along the graphene-SiO₂ interface is blocked, which is observed to result in a reduction in permeation rate by a factor of 10⁴. The experiments thus demonstrate that gas flow along the graphene-SiO₂ interface tends to dominate the leak rate in unsealed graphene nanodrums. Moreover, the presented sealing method enables the study of intrinsic gas leakage through graphene membranes and can enable hermetic graphene membranes for pressure sensing applications.

Two-dimensional (2D) materials with strong in-plane anisotropy are of interest for enabling orientation-dependent, frequency-tunable, optomechanical devices. However, black phosphorus (bP), the 2D material with the largest anisotropy to date, is unstable as it degrades in air. In this work we show that As₂S₃ is an interesting alternative, with a similar anisotropy to bP, while at the same time having a much higher chemical stability. We probe the mechanical and optical anisotropy in As₂S₃ by three distinct angular-resolved experimental methods: Raman spectroscopy, atomic force microscopy (AFM), and resonance frequency analysis. Using a dedicated angle-resolved AFM force-deflection method, an in-plane anisotropy factor of EaEc=1.7 is found in the Young's modulus of As₂S₃ with E_a-axis = 79.1 ± 10.1 GPa and E_c-axis = 47.2 ± 7.9 GPa. The high mechanical anisotropy is also shown to cause up to 65% difference in the resonance frequency, depending on crystal orientation and aspect ratio of membranes.

We explore the superconducting phase diagram of the two-dimensional electron system at the LaAlO3/SrTiO3 interface by monitoring the frequencies of the cavity modes of a coplanar waveguide resonator fabricated in the interface itself. We determine the phase diagram of the superconducting transition as a function of the temperature and electrostatic gating, finding that both the superfluid density and the transition temperature follow a dome shape but that the two are not monotonically related. The ground state of this two-dimensional electron system is interpreted as a Josephson junction array, where a transition from long- to short-range order occurs as a function of the electronic doping. The synergy between correlated oxides and superconducting circuits is revealed to be a promising route to investigate these exotic compounds, complementary to standard magnetotransport measurements.

Electro-optic modulators based on micro-electromechanical systems have found success as elements for optical projectors, for simplified optical spectrometers, and as reflective-type screens that make use of light interference (Interferometric Modulator Display technology). The latter concept offers an exciting avenue for graphene nanomechanical structures to replace classical micro-electromechanical devices and bring about enhancement in performance, especially switching speed and voltage. In this work we study the optical response of electrically actuated graphene drumheads by means of spectrometric and stroboscopic experiments. The color reproducibility and speed of these membranes in producing the desired electro-optic modulation makes them suitable as pixels for high refresh rate displays. As a proof of concept, we demonstrate a Graphene Interferometric Modulator Display prototype with 5 μm-in-diameter pixels that compose a high resolution image (2500 pixels per inch)-equivalent to a 5″ display of 12K-whose color can be changed at frame rates of at least 400 Hz.

We report on the development of a pneumatically coupled graphene membrane system, comprising of two circular cavities connected by a narrow trench. Both cavities and the trench are covered by a thin few-layer graphene membrane to form a sealed dumbbell-shaped chamber. Local electrodes at the bottom of each cavity allow for actuation of each membrane separately, enabling electrical control and manipulation of the gas flow inside the channel. Using laser interferometry, we measure the displacement of each drum at atmospheric pressure as a function of the frequency of the electrostatic driving force and provide a proof-of-principle of using graphene membranes to pump attolitre quantities of gases at the nanoscale.

We report on a pneumatically coupled graphene pump system, comprising two cylindrical cavities of 3 femtoliter connected by a narrow trench, all covered by a thin few-layer graphene membrane. Local electrodes at the bottom of each cavity enable electrostatic pressure control and manipulation of gas flow through the channel. Using laser interferometry, we measure graphene displacement as a function of driving amplitude and frequency, thus providing proof-of-principle for using graphene membranes to pump attoliter quantities of gases and demonstrating pneumatic actuation at the nanoscale.

Chemical functionalization is a powerful approach to tailor the physical and chemical properties of two-dimensional (2D) materials, increase their processability and stability, tune their functionalities and, even, create new 2D materials. This is typically achieved through post-synthetic functionalization by anchoring molecules on the surface of an exfoliated 2D crystal, but it inevitably alters the long-range structural order of the material. Here we present a pre-synthetic approach that allows the isolation of crystalline, robust and magnetic functionalized monolayers of coordination polymers. A series of five isostructural layered magnetic coordination polymers based on Fe(ii) centres and different benzimidazole derivatives (bearing a Cl, H, CH₃, Br or NH₂ side group) were first prepared. On mechanical exfoliation, 2D materials are obtained that retain their long-range structural order and exhibit good mechanical and magnetic properties. This combination, together with the possibility to functionalize their surface at will, makes them good candidates to explore magnetism in the 2D limit and to fabricate mechanical resonators for selective gas sensing.

For the study and application of graphene membranes, it is essential to have means to control their resonance frequency and temperature. Here, we present an on-chip heater platform for local tuning of in-plane tension in graphene mechanical resonators. By Joule heating of a metallic suspension ring we show thermomechanical resonance frequency tuning in a few-layer (FL) graphene nanodrum, which is accompanied by an increase in its quality factor, which we attribute to the increase of the in-plane tension. The in situ control of temperature, in-plane tension, resonance frequency, and quality factor of suspended two-dimensional (2D) nanodrums makes this device a unique platform for investigating the origin of dissipation in these ultrathin structures and can be of fundamental importance for studying the thermal properties of 2D materials. Moreover, by simultaneously controlling the heater and the backgate voltage, we can independently control the resonance frequency and quality factor, which is of great importance for applications in sensors and resonant mechanical filters.

Superconducting coplanar waveguide (CPW) resonators are powerful and versatile tools used in areas ranging from radiation detection to circuit quantum electrodynamics. Their potential for low intrinsic losses makes them attractive as sensitive probes of electronic properties of bulk materials and thin films. Here we use superconducting MoRe CPW resonators to investigate the high-frequency (up to 0.3 GHz) and low-temperature (down to 3.5 K) permittivity of SrTiO3, a nonlinear dielectric on the verge of a ferroelectric transition (quantum paraelectricity). We perform a quantitative analysis of its dielectric properties as a function of external dc bias (up to ±15V), rf power, and mode number and discuss our results within the framework of the most recent theoretical models. We also discuss the origin of a fatigue effect that reduces the tunability of the dielectric constant of SrTiO3, which we relate to the presence of oxygen vacancies.

Contactless characterization of mechanical resonances using Fabry-Perot interferometry is a powerful tool to study the mechanical and dynamical properties of atomically thin membranes. However, amplitude calibration is often not performed or only possible by making assumptions on the device parameters such as its mass or the temperature. In this work, we demonstrate a calibration technique that directly measures the oscillation amplitude by detecting higher harmonics that arise from nonlinearities in the optical transduction. Employing this technique, we calibrate the resonance amplitude of two-dimensional nanomechanical resonators, without requiring knowledge of their mechanical properties, actuation force, geometric distances, or the laser intensity.

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 τ 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 τ, 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.