Ultrasonic nodal chains in topological granular metamaterials

Abstract

Three-dimensional (3D) Weyl and Dirac semimetals garner considerable attention in condensed matter physics due to the exploration of entirely new topological phases and related unconventional surface states. Nodal line and ring semimetals, on the other hand, can facilitate 3D band crossings characterized by nontrivial links such as coupled chains and knots that are protected by the underlying crystal symmetry. Experimental complexities and detrimental effects of the spin-orbit interaction, among others, pose great challenges for the advancement that can be overcome with other systems such as bosonic lattices. Here we demonstrate that a 3D mechanical metamaterial made of granular beads hosts multiple intersecting nodal rings in the ultrasonic regime. By unveiling these yet unseen classical topological phases, we discuss the resilience of the associated novel surface states that appear entirely unaffected to the type of crystal termination, making them a promising platform in ultrasonic devices for non-destructive testing and material characterization.