Symmetry of rigid-layer modes: Raman and infrared activity

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. •Rigid layer modes of all possible layered structures are classified by symmetry.•Raman and infrared active ones are pointed out, counted and associated to symmetry quantum numbers.•Impact of symmetry to inter layer coupling is analyzed.•The rigid layer modes are related to the exact solutions of alternating and uniform linear chain model.•Applicability of the results to the currently most studied 2D materials is discussed.