Collective modes of twisted van der Waals materials

Rotationally misalignment profoundly modifies electronic and lattice properties of van der Waals materials. If the twist angle between adjacent layers is small, a periodic network of dislocations (solitons) delineating large commensurate domains appears. We show that the solitons can have a surprisingly strong influence on collective modes of the system, e.g., plasmon- and phonon-polaritons. In particular, a twisted bilayer graphene can act as a photonic crystal for either two-dimensional or one-dimensional plasmon modes. On the other hand, in twisted boron nitride, the solitons can induce shift and splitting of the phonon-polaritons. Our theory provides explanation of recent nano-optical experiments done with twisted van der Waals heterostructures.