Tunable Nonlinear Landscapes in Graphene Nanoelectromechanical Systems

Abstract

Nonlinear nanomechanical resonators give convenient solid-state access to classical analogs of extreme nonlinear optics and to phononic signal processing. Here we report integer high-harmonic generation and phononic frequency combs in a suspended monolayer graphene drum. A gate voltage breaks the out-of-plane symmetry of the membrane and tunes its fundamental flexural mode onto a 1:2 internal resonance with a higher mode at twice the frequency, where the quadratic coupling between the two modes becomes large. A single drive tone then generates phase-locked integer harmonics in sequence, and at larger drive these fill in to a dense frequency comb. Raising the drive further, we find a reverse period-doubling transition: the comb spacing doubles, the line density halves, and energy flows back into the even-order comb lines. The measured spectra yield the quadratic ($\zeta$) and cubic ($\beta$) nonlinear coefficients of the membrane. These results show how the tunable nonlinear landscape of graphene supports distinct dynamical regimes on demand, allowing a single gated device to act in turn as a frequency multiplier, a broadband comb source, and a chaotic generator.