While there has been tremendous progress in realizing high frequency, tunable, stable, atomically thin microresonators from individual two-dimensional (2D) materials and their combinations, their poor mechanical resonance quality at room temperature is still an open area of research. Taking a multiscale modeling approach and graphene as a representative 2D system, we show that intrinsic dissipation due to flexural mode coupling can explain the room temperature behavior. The inverse quality factor $Q^{-1}$, a nondimensional measure of dissipation, solely due to the coupling with nanometer wavelength flexural modes in the structure is found to be nonlinear in the vibration amplitude, and also dependent on the resonator size, strain, and temperature. At lower amplitudes and submicron to micron sizes, however, $Q^{-1}$ mediated by coupling with the submicro- to micrometer wavelength flexural modes dominates. This $Q^{-1}$ is amplitude independent, and bears a similar implicit dependence on the temperature ($T$) and inverse strain ($1/ϵ$), suggesting that $T/ϵ$ is a better metric to characterize the dissipation.

中文翻译：

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通过多尺度方法揭示二维材料谐振器中的模式耦合引起的固有耗散

尽管从单个二维（2D）材料及其组合实现高频，可调谐，稳定，原子薄的微谐振器已经取得了巨大进步，但其在室温下较差的机械谐振质量仍是一个有待研究的领域。以多尺度建模方法和石墨烯为代表的2D系统，我们表明由于弯曲模式耦合引起的固有耗散可以解释室温行为。逆品质因数${问}^{-\mathrm{1个}}$，仅由于与结构中的纳米波长弯曲模式耦合而导致的无量纲的耗散量度在振动幅度上是非线性的，并且还取决于谐振器的尺寸，应变和温度。但是，在较低的振幅和亚微米到微米的尺寸下，${问}^{-\mathrm{1个}}$通过与亚微米至微米的波长耦合而介导的弯曲模式占主导地位。这个${问}^{-\mathrm{1个}}$ 与振幅无关，并且对温度具有类似的隐式依赖关系（$Ť$）和反应变（$\mathrm{1个}/ϵ$），表明 $Ť/ϵ$ 是表征耗散的更好指标。