Dynamically-enhanced strain in atomically-thin resonators

Owing to their low mass and outstanding mechanical figures of merit, graphene and related two-dimensional (2D) materials are ideal nano-electro-mechanical systems, for applications in mass and force sensing but also for studies of heat transport, non-linear mode coupling and optomechanical interactions. At the same time, 2D materials are endowed with unique electronic, optical and phononic properties, suitable for hybrid systems that couple their elementary excitations (excitons, phonons) and/or degrees of freedom (spin, valley) to macroscopic flexural vibrations. The built-in nature of such hybrid systems may yield enhanced strain-mediated coupling as compared to bulkier hybrid systems, e.g., comprising a single quantum emitter coupled to a nano-mechanical resonator. Here, using micro-Raman scattering spectroscopy on circular drums made from pristine graphene monolayers, we demonstrate dynamical softening of optical phonons induced by the macroscopic flexural motion of graphene. This softening is an unambiguous fingerprint of dynamically-induced tensile strain that reaches values up to 4x10-4 under strong non-linear driving. These anomalously large strains exceed the time-averaged values predicted for harmonic vibrations with the same root mean square (RMS) amplitude by more than one order of magnitude and are proportional to the non-linear frequency shift of the mechanical resonance of the drum. Our work provides an impetus for modelling non-linear dynamics in atomically-thin resonators beyond elasticity theory and holds promise for dynamical strain engineering and dynamical strain-mediated control of light-matter interactions, single-photon emission or magnetic order in 2D materials and related heterostructures.