  Due to their low mass and long coherence times, nanomechanical resonators
have many applications, from biomolecule mass sensing to hybrid quantum
interfaces. In many instances the performance is limited by internal material
damping. Crystalline materials promise lower material dissipation, however due
to fabrication challenges, amorphous materials are more commonly utilized.
Crystalline silicon carbide (SiC) is particularly appealing due to its
exquisite mechanical, electrical and optical properties, but to-date exhibits
higher nanomechanical dissipation than both amorphous and other crystalline
materials. To address this, we fabricate nanomechanical resonators thinned from
bulk monocrystalline 4H-SiC. Characterization of multiple resonators of
different sizes and thicknesses, allows us to discern the surface and
volumetric contributions to dissipation. We measure mechanical dissipation
rates as low as 2.7 mHz, more than an order-of-magnitude lower than any
previous crystalline SiC resonator, yielding quality factors as high as 20
million at room temperature. We also quantify the nonlinear dissipation of SiC
nanomechanical resonators for the first time, finding that it is lower than
other materials. This promises higher sensitivity in applications such as mass
sensing. By achieving exceptionally low dissipation in SiC resonators, our work
provides a path towards improved performance in sensing and other applications.
