Dynamic twisting and imaging of moir\'e crystals

The electronic band structure is an intrinsic property of solid-state materials that is intimately connected to the crystalline arrangement of atoms. Moir\'e crystals, which emerge in twisted stacks of atomic layers, feature a band structure that can be continuously tuned by changing the twist angle between adjacent layers. This class of artificial materials blends the discrete nature of the moir\'e superlattice with intrinsic symmetries of the constituent materials, providing a versatile platform for investigation of correlated phenomena whose origins are rooted in the geometry of the superlattice, from insulating states at "magic angles" to flat bands in quasicrystals. Here we present a route to mechanically tune the twist angle of individual atomic layers with a precision of a fraction of a degree inside a scanning probe microscope, which enables continuous control of the electronic band structure in-situ. Using nanostructured rotor devices, we achieve the collective rotation of a single layer of atoms with minimal deformation of the crystalline lattice. In twisted bilayer graphene, we demonstrate nanoscale control of the moir\'e superlattice period via external rotations, as revealed using piezoresponse force microscopy. We also extend this methodology to create twistable boron nitride devices, which could enable dynamic control of the domain structure of moir\'e ferroelectrics. This approach provides a route for real-time manipulation of moir\'e materials, allowing for systematic exploration of the phase diagrams at multiple twist angles in a single device