Phonons and Phase Symmetries in Non-Symmorphic Twisted and Layered Materials

Structural complexity underlies a variety of novel quasiparticle behaviors that can have profound impacts on material functionalities. Here I will discuss the role of structural twisting and translational symmetries in determining the vibrational behaviors of non-symmorphic chiral and achiral materials and how these translate into spectral features and functionalities. We advance a dynamical theory that incorporates the various symmetries internal to the lattice unit cell directly into the description of the phonon frequencies and eigenvectors. This naturally elucidates phase conservation relations in twisted structures and layered materials. We apply this theory to build insights into vibrational dynamical structure factors and spectral observations from inelastic neutron and x-ray scattering experiments, and provide a fresh perspective on symmetry-enforced crossings, quasiparticle interactions, and band topologies.<br/><br/>L.L. acknowledges support from the U. S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division.