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Silicon nitride membrane resonators at millikelvin temperatures with quality factors exceeding $10^8$

We study mechanical dissipation of the fundamental mode of millimeter-sized, high quality-factor ($Q$) metalized silicon nitride membranes at temperatures down to 14 mK using a three-dimensional optomechanical cavity. Below 200 mK, high-$Q$ modes of the membranes show a diverging increase of $Q$ with decreasing temperature, reaching $Q=1.27\times10^8$ at 14 mK, an order of magnitude higher than reported before. The ultra-low dissipation makes the membranes highly attractive for the study of optomechanics in the quantum regime, as well as for other applications of optomechanics such as microwave to optical photon conversion.