Spatial Mapping and Analysis of Graphene NEMS Resonator Networks

Networks of nanoelectromechanical (NEMS) resonators are useful analogs for a variety of many-body systems and enable disruptive applications in sensing, phononics, and mechanical information processing. A challenge toward realizing practical NEMS networks is the ability to characterize the constituent resonator building blocks and their coupling. In this work, we demonstrate a scalable optical technique to spatially map graphene NEMS networks and read out the fixed-frequency collective response as a single vector. Using the response vectors, we introduce an efficient algebraic formalism to accurately quantify the site-specific elasticity, mass, damping, and coupling parameters of network clusters. In a departure from multiple regression, our formalism uses just two measured response vectors to fully characterize the network parameters, all without a priori parameter estimates or iterative computation. We apply this suite of techniques to single-resonator and coupled-pair clusters, finding excellent agreement with expected parameter values and broader spectral response. Our approach offers a new, non-regressive means to accurately characterize a range of classical and quantum resonator systems and fills in a vital gap for programmable NEMS networks.