  In the field of phononics, periodic patterning controls vibrations and
thereby the flow of heat and sound in matter. Bandgaps arising in such phononic
crystals realize low-dissipation vibrational modes and enable applications
towards mechanical qubits, efficient waveguides, and state-of-the-art sensing.
Here, we combine phononics and two-dimensional materials and explore the
possibility of manipulating phononic crystals via applied mechanical pressure.
To this end, we fabricate the thinnest possible phononic crystal from monolayer
graphene and simulate its vibrational properties. We find a bandgap in the MHz
regime, within which we localize a defect mode with a small effective mass of
0.72 ag = 0.002 $m_{physical}$. Finally, we take advantage of graphene's
flexibility and mechanically tune a finite size phononic crystal. Under
electrostatic pressure up to 30 kPa, we observe an upshift in frequency of the
entire phononic system by more than 350%. At the same time, the defect mode
stays within the bandgap and remains localized, suggesting a high-quality,
dynamically tunable mechanical system.
