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Discrete time crystals (DTCs) are emergent non-equilibrium phases of periodically driven many-body systems, with potential applications ranging from quantum computing to sensing and metrology. There has been significant recent interest in understanding mechanisms leading to DTC formation and a search for novel DTC phases beyond subharmonic entrainment. Here, we report observation of multiple DTC phases in a nanoelectromechanical system (NEMS) based on coupled graphene and silicon nitride membranes. We confirm the time-crystalline nature of these symmetry broken phases by establishing their many-body characters, long-range time and spatial order, and rigidity against parameter fluctuation or noise. Furthermore, we employ controlled mechanical strain to drive the transitions between phases with different symmetries, thereby mapping the emergent time-crystalline phase diagram. Overall, our work takes a step towards establishing time crystals as a system with complexity rivaling that of solid state crystals., Comment: 8 pages, 4 figures

High quality factor mechanical resonators have shown great promise in developing classical or quantum technologies. Simultaneously, progress has been made in developing controlled mechanical nonlinearity. Here we combine these two directions of progress in a single platform consisting of coupled Silicon Nitride (SiNx) and graphene mechanical resonators. We show that nonlinear response can be induced on a large area SiNx resonator mode and can be efficiently controlled by coupling it to a gate-tunable, freely suspended graphene mode. The induced nonlinear response of the hybrid modes, as measured on the SiNx resonator surface is giant, with one of the highest measured Duffing constants. We observe a novel phononic frequency comb which we use as an alternate validation of the measured values, along with numerical simulations which are in overall agreement with measurements.

There is a recent surge of interest in amplification and detection of tiny motion in the growing field of opto and electro mechanics. Here, we demonstrate widely tunable, broad bandwidth and high gain all-mechanical motion amplifiers based on graphene/Silicon Nitride (SiNx) hybrids. In these devices, a tiny motion of a large-area SiNx membrane is transduced to a much larger motion in a graphene drum resonator coupled to SiNx. Furthermore, the thermal noise of graphene is reduced (squeezed) through parametric tension modulation. The parameters of the amplifier are measured by photothermally actuating SiNx and interferometrically detecting graphene displacement. We obtain displacement power gain of 38 dB and demonstrate 4.7 dB of squeezing resulting in a detection sensitivity of 3.8 fm per square root Hz, close to the thermal noise limit of SiNx., Comment: 7 pages, 4 figures and supplementary information

We investigated the effect of out-of-plane crumpling on the mechanical response of graphene membranes. In our experiments, stress was applied to graphene membranes using pressurized gas while the strain state was monitored through two complementary techniques: interferometric profilometry and Raman spectroscopy. By comparing the data obtained through these two techniques, we determined the geometric hidden area which quantifies the crumpling strength. While the devices with hidden area $\sim0~\%$ obeyed linear mechanics with biaxial stiffness $428\pm10$ N/m, specimens with hidden area in the range $0.5-1.0~\%$ were found to obey an anomalous Hooke's law with an exponent $\sim0.1$.

Free-standing graphene is inherently crumpled in the out-of-plane direction due to dynamic flexural phonons and static wrinkling. We explore the consequences of this crumpling on the effective mechanical constants of graphene. We develop a sensitive experimental approach to probe stretching of graphene membranes under low applied stress at cryogenic to room temperatures. We find that the in-plane stiffness of graphene is between 20 and 100 N/m at room temperature, much smaller than 340 N/m (the value expected for flat graphene). Moreover, while the in-plane stiffness only increases moderately when the devices are cooled down to 10 K, it approaches 300 N/m when the aspect ratio of graphene membranes is increased. These results indicate that softening of graphene at temperatures less than 400 K is caused by static wrinkling, with only a small contribution due to flexural phonons. Together, these results explain the large variation in reported mechanical constants of graphene devices and paves the way towards controlling their mechanical properties., Comment: 9 pages, 5 figures