Ultracoherent diamond nanomechanical resonators protected by a phononic bandgap

Ultracoherent nanomechanical resonators are essential components in optomechanics, spin-mechanics and phonon-mediated hybrid quantum systems. In silicon and silicon-nitride based systems, phononic bandgap structures have been proven effective in protecting a mechanical mode from coupling to its surrounding environment. Here we present the design, fabrication and characterization of diamond-based nanomechanical resonators embedded in a square phononic crystal lattice with mechanical Q-factors exceeding 10^6 at frequencies as high as 100MHz for out-of-plane modes. We show that the robust protection from a phononic bandgap can lead to a three-orders-of-magnitude increase in the mechanical quality factors. The ultracoherent mechanical modes can be coupled to color centers that feature excellent spin and optical properties, leading to a promising hybrid quantum system for pursuing spin-phonon coupling studies.