Topological nodal line states in three-dimensional ball-and-stick sonic crystals

Nodal line states in electronic systems are the extended band crossings in three-dimensional (3D) momentum space, which recently has been widely explored in classical systems in analogs. With the Dirac cones in two-dimensional (2D) hexagonal lattices, the linear degeneracy points in the stacking 2D hexagonal lattices (3D lattices) are elongated into degeneracy lines in the momentum space. In this work, we show that by coupling the stacked hexagonal lattices with the time-reversal symmetry and inversion symmetry protected, degeneracy points will form a closed nodal ring in the momentum space in the strong coupling regime. We observe flat drumhead dispersion surfaces in the band gaps, which verifies the existence of the intriguing nodal line states. Based on full-wave simulations, we show the field confinement at the truncated surface and the field enhancement due to the large density of states in flat bands. Furthermore, topological robustness of the drumhead surface states is investigated against various randomly distributed defects, such as site disorders and hopping disorders. Our work may serve as the platform of the sonic-crystal based semimetal for versatile applications like sound trapping, vibration isolation, and absorption.