Strain engineering for a gigahertz mechanical resonator based on two-dimensional atomic-layer phononic crystals

Achieving both ultrahigh quality $Q$ and high frequency simultaneously in mechanical resonators is challenging due to the positive correlation between loss and frequency. Graphene, a two-dimensional (2D) material with single-atomic-layer thickness and exceptional mechanical properties, is capable of satisfying the material requirements of emerging dissipation dilution and strain engineering. By combining graphene with dissipation dilution and strain engineering in phononic crystals (PnCs), we propose PnC mechanical resonators possessing ultrahigh $Q$ and frequency simultaneously. Owing to the substantial prestress and the ultrahigh structural aspect ratio (feature size vs thickness) conferred by graphene, a tapered PnC resonator with the support of strain engineering breaks the upper limit of the theoretical $Q$ of soft clamping at room temperature. It benefits from the colocalization of the displacement and stress distribution of the resonant mode, enhancing $Q$ to $6.8\ifmmode\times\else\texttimes\fi{}{10}^{8}$ at 3.3 GHz. In addition, such 2D material PnC resonators can have efficient electrical tunability, including higher frequency and $Q$, via a simple gate setting. This innovative mechanical resonator holds promise for future phononic information processing, sensing, and quantum storage.