Nonlinear coupling of closely spaced modes in atomically thin MoS2 nanoelectromechanical resonators.

Nanoelectromechanical systems (NEMS) incorporating atomic or molecular layer van der Waals materials can support multimode resonances and exotic nonlinear dynamics. Here we investigate nonlinear coupling of closely spaced modes in a bilayer (2L) molybdenum disulfide (MoS₂) nanoelectromechanical resonator. We model the response from a drumhead resonator using equations of two resonant modes with a dispersive coupling term to describe the vibration induced frequency shifts that result from the induced change in tension. We employ method of averaging to solve the equations of coupled modes and extract an expression for the nonlinear coupling coefficient (λ) in closed form. Undriven thermomechanical noise spectral measurements are used to calibrate the vibration amplitude of mode 2 (a₂) in the displacement domain. We drive mode 2 near its natural frequency and measure the shifted resonance frequency of mode 1 (f_1s) resulting from the dispersive coupling. Our model yields λ = 0.027 ± 0.005 pm^-2 · μs^-2 from thermomechanical noise measurement of mode 1. Our model also captures an anomalous frequency shift of the undriven mode 1 due to nonlinear coupling to the driven mode 2 mediated by large dynamic tension. This study provides a direct means to quantifying λ by measuring the thermomechanical noise in NEMS and will be valuable for understanding nonlinear mode coupling in emerging resonant systems.