Symmetry and degeneracy of phonon modes for periodic structures with glide symmetry

A large class of phononic crystals and mechanical metamaterials exhibit glide symmetry that dictates their functionality or exceptional performance. The glide symmetry gives rise to a number of intriguing phenomena like sticking-bands and degeneracy in the phononic band structures. Fully understanding of these phenomena demands analysis of the phonon modes' symmetry property, which is, however, a challenging task since it involves nonsymmorphic space group analysis and special treatment of the Brillouin zone boundary. Therefore, this work introduces a systematic group-theoretical procedure determining the symmetry of phonon modes for periodic structures with glide symmetry. By taking the p4g group as an example, the symmetry of phonon modes is discussed by deriving the small representations for high symmetry k-points, and different types of degeneracies are elucidated. This work provides insight into the role of glide symmetry on phononic band structures and guides the symmetry analysis of periodic structures of other types.