The possibility of realizing an electrostatically induced phononic crystal is investigated numerically in an acoustic waveguide based on a graphene sheet that is suspended over periodically arrayed electrodes. The application of dc voltage to these electrodes exerts electrostatic force on the graphene and this results in the periodic formation of stress in the waveguide structure in a non-invasive way, unlike the cases with mass loading and air holes. This non-invasive scheme enables a bandgap, namely a phononic crystal, to be created in the waveguide that can be used to dynamically tune the acoustic transparency in the medium. Our approach will allow the dispersion relation to be locally modified, thus modulating the temporal response of traveling acoustic phonon waves. This novel phonon architecture is promising in terms of realizing the advanced control of phonon dynamics such as waveform and dissipation engineering in the device.

12 pages, 5 figures