This work was supported by Chalmers' Area of Advance Nano, the Knut and Alice Wallenberg Foundation through a Wallenberg Academy Fellowship (W.W.) and the Wallenberg Center for Quantum Technology (WACQT, A.C.), the Swedish Research Council (VR projects No. 2018-05061 and 2019-04946), and the QuantERA project C'MON-QSENS! H.P. acknowledges funding by the European Union under the project MSCA-PF-2022-OCOMM. Samples were fabricated in the Myfab Nanofabrication Laboratory at Chalmers and analyzed in the Chalmers Materials Analysis Laboratory. Simulations were performed on resources provided by the National Academic Infrastructure for Supercomputing in Sweden (NAISS) and the Swedish National Infrastructure for Computing (SNIC) at Tetralith partially funded by the Swedish Research Council through grant agreements no. 2022-06725 and no. 2018-05973.

Data used for figures in "Integrated microcavity optomechanics with a suspended photonic crystal mirror above a distributed Bragg reflector" Sushanth Kini Manjeshwar et.al (arXiv:2305.13511)