Negative nonlinear damping of a multilayer graphene mechanical resonator

We experimentally investigate the nonlinear response of a multilayer graphene resonator using a superconducting microwave cavity to detect its motion. The radiation pressure force is used to drive the mechanical resonator in an optomechanically induced transparency configuration. By varying the amplitudes of drive and probe tones, the mechanical resonator can be brought into a nonlinear limit. Using the calibration of the optomechanical coupling, we quantify the mechanical Duffing nonlinearity. By increasing the drive force, we observe a decrease in the mechanical dissipation rate at large amplitudes, suggesting a negative nonlinear damping mechanism in the graphene resonator. Increasing the optomechanical backaction further, we observe instabilities in the mechanical response.

Figure 1

(a) A scanning electron micrograph of a multilayer graphene (10 nm thick) drum-shaped resonator coupled to a superconducting microwave cavity (not shown here). Graphene resonator is suspended 150 nm above the bottom gate electrode (adapted from Ref. [5]). (b) Schematic diagram of the device: graphene resonator couples external microwave radiation to the cavity by forming a coupling capacitor.

Figure 2

(a) Schematic showing the idea of radiation pressure driving. Due to the optomechanical coupling, driving the cavity with a strong tone near ${\omega }_d={\omega }_c-{\omega }_m$ and a weak probe tone ${\omega }_p$ near ${\omega }_c$ exerts a radiation pressure force on the mechanical resonator at ${\omega }_m$. The strength of radiation pressure force is controlled by the product of probe tone and the drive tone amplitudes. (b) Illustration of the cavity reflection coefficient in the presence of a strong sideband drive. The optomechanical interaction produces an absorption feature in the cavity response. (c) A zoomed-in view of the theoretically expected OMIA feature of a mechanical resonator that includes a Duffing nonlinearity in the linear and nonlinear regimes.

Figure 3

Forward (red) and reverse (cyan) frequency sweep measurement of OMIA feature of the multilayer graphene drum showing mechanical response at various probe and drive powers. The probe photons are swept from $n_p=2.5\times {10}^5$ to $3.14\times {10}^6$ in 1 dB steps (top to bottom). Number of drive photons $n_d$ is fixed at $2.5\times {10}^7$ ($C\sim 0.40$) for panel (a) and $1.0\times {10}^8$ ($C\sim 1.24$) photons for panel (b). The evolution of nonlinear response accompanied by the hysteresis can be clearly seen as probe power is increased (top to bottom). Panel (b) shows instability points as sharp dips appearing at large probe power. For clarity, measurements in (a) and (b) are plotted with offsets of $-30$ dB and $-9$ dB, respectively.

Figure 4

(a) Measurement of $S_{11}$ showing strong nonlinear response (red curve) together with numerically fitted curve (gray) for $n_d=2.5\times {10}^7$. (b), (c) Extracted linear dissipation rate ${\gamma }_m$ plotted against mechanical amplitude for $n_d=2.5\times {10}^7$ and for $1.0\times {10}^8$, respectively.