Theory of dynamical structure factors in complex twisted materials

Structural complexity underlies a variety of novel quasiparticle behaviors that can have profound impacts on material functionalities. Here we intimately examine the theory of lattice dynamical spectra of ‘twisted’ materials with combined rotational and translational symmetries. We advance a dynamical theory that incorporates the twist symmetry directly into the description of the phonon frequencies and eigenvectors, which naturally elucidates the underlying angular momenta of phonon bands. We apply this theory to build insights into dynamical structure factors and spectral observations from inelastic neutron and x-ray scattering experiments.