Nodal rings and drumhead surface states in phononic crystals

Three-dimensional topological nodal lines, the touching curves of two bands in momentum space, which give rise to drumhead surface states, provide an opportunity to explore a variety of exotic phenomena. However, solid evidence for a flat drumhead surface state remains elusive. In this paper, we report a realization of three-dimensional nodal line dispersions and drumhead surface states in phononic crystal. Profiting from its macroscopic nature, the phononic crystal permits a flexible and accurate fabrication for materials with ring-like nodal lines and drumhead surface states. Phononic nodal rings of the lowest two bands and, more importantly, topological drumhead surface states are unambiguously demonstrated. Our system provides an ideal platform to explore the intriguing properties of acoustic waves endowed with extraordinary dispersions.