Symmetry of rigid-layer modes: Raman and infrared activity

Abstract

Symmetry of multilayer structures is analyzed in order to count and specify Raman and infrared active rigid-layer vibrational modes. Effective Hessian matrix of rigid-layer dynamics corresponds to simple model of linear chain (composed of monolayers); its symmetry, derived from the symmetry of the multilayer, assigns the modes and determines their activity. These general results are illustrated on currently most studied (multi)layered structures: graphene, transition metal dichacogenides, phosphorene, boron nitride and graphene based materials.