Tunable Nonlinear Landscapes in Graphene Nanoelectromechanical Systems

Nonlinear nanomechanical resonators give convenient solid-state access to classical analogs of extreme nonlinear optics and to phononic signal processing. Here we report integer harmonic generation, phononic frequency sideband comb, and reverse period-doubling dynamics in a single platform of a suspended graphene resonator. A gate voltage breaks the out-of-plane symmetry of the membrane and establishes a 1:2 internal resonance between mechanical resonators. Under a single drive tone, integer harmonics are generated sequentially, forming a dense sideband frequency comb at larger drive. 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 spectrum yields the quadratic (ζ) and cubic (β) nonlinear coefficients of the membrane. These results demonstrate electrical control of several nonlinear landscapes in a single graphene resonator, enabling frequency multiplication, sideband comb generation, and broadband irregular motion.