Tunable Fano Resonance and Frequency Locking in a Graphene-SiNx Hybrid Nanomechanical Resonator
Fano resonances, arising from the interference between discrete and continuum states, are observed across a wide range of quantum and classical systems. Here, we report the experimental observation of Fano resonances in a graphene SiNx hybrid nanomechanical system modeled as coupled oscillators. The broad, low quality factor graphene mode plays the role of the continuum, while the dense comb of sharp, high quality factor SiNx modes provides the discrete states. The inter-mode detuning is tunable via a DC gate voltage, enabling dynamic control of the Fano resonance: we demonstrate gate controlled switching of both the sign and the magnitude of the Fano asymmetry parameter $q$, in quantitative agreement with a coupled oscillator theory that predicts $q=-\cot\phi$, with $\phi$ the phase of the continuum response. At strong drive, the graphene mode enters the Duffing regime and its jump-down frequency locks to successive SiNx modes, producing a staircase of drive insensitive frequency plateaus; a weak seeding tone deterministically switches the resonator between adjacent locked states. The dense SiNx mode thus acts, in the linear regime, as the discrete states of a tunable Fano interferometer and, in the nonlinear regime, as a frequency ruler that stabilizes and quantizes the graphene oscillation. This platform offers a controllable mechanical realization of Fano interference and opens new avenues for high resolution hybrid resonant sensors and stable nanomechanical frequency references.