High-quality-factor viscoelastic nanomechanical resonators from moiré superlattices.

The moiré superlattice, created by stacking van der Waals layered materials with rotational misalignments, exhibits a multitude of emergent correlated phenomena ranging from superconductivity to Mott insulating states. In addition to exotic electronic states, the intricate networks of incommensurate lattices may give rise to polymer-like viscoelasticity, which combines the properties of both elastic solids and viscous fluids. This phenomenon may enrich the dynamics of nanomechanical resonators, in which viscoelasticity has not played a role thus far. Here, we report on a controllable hysteretic response of the nanomechanical vibrations in twisted bilayer graphene membranes, which we attribute to viscoelasticity. Accompanying this hysteretic response, we measure unusually large mechanical quality factors Q reaching a remarkably high value of  ~1900 at room temperature. We interpret the enhancement of Q as a signature of dissipation dilution, a phenomenon of considerable interest that has recently been harnessed in quantum optomechanical systems. Viscoelasticity features a "lossless" potential that overcomes the corrugation registry and reinforces such a dissipation dilution. Our work introduces the moiré superlattice as a promising system for viscoelasticity engineering through rotating angles and for observing emergent nanoelectromechanical couplings.