Mechanically-tunable bandgap closing in 2D graphene phononic crystals

We present a tunable phononic crystal which undergoes a phase transition from mechanically insulating to mechanically transmissive (metallic). Specifically, in our simulations for a phononic lattice under biaxial tension ($\sigma_{xx} =\sigma_{yy}$ = 0.01 N$/$m), we find a bandgap for out-of-plane phonons in the range of 48.8 - 56.4 MHz, which we can close by increasing the degree of tension uniaxiality ($\sigma_{xx} / \sigma_{yy}$) to 1.7. To manipulate the tension distribution, we design a realistic device of finite size, where $\sigma_{xx} / \sigma_{yy}$ is tuned by applying a gate voltage to a phononic crystal made from suspended graphene. We show that the phase transition can be probed via acoustic transmission measurements and that the phononic bandgap persists even after the inclusion surface contaminants and random tension variations present in realistic devices. The proposed system acts as a transistor for phonons with an on/off ratio of $10^5$ (100 dB suppression) and is thus a valuable extension for phonon logic applications. In addition, this mechanical analogue to a metal-insulator transition (mMIT) allows tunable coupling between mechanical entities (e.g. mechanical qubits).