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Three-dimensional (3D) Weyl and Dirac semimetals garner considerableattention in condensed matter physics due to the exploration of entirely newtopological phases and related unconventional surface states. Nodal line andring semimetals on the other hand can facilitate 3D band crossingscharacterized by nontrivial links such as coupled chains and knots that areprotected by the underlying crystal symmetry. Experimental complexities,detrimental effects of the spin-orbit interaction, along with the merging ofthe underlying surface states into the bulk pose great challenges for growingadvancements, but fortunately enable other systems, such as bosonic lattices,as ideal platforms to overcome these obstacles. Here we demonstrate a 3Dmechanical metamaterial made of granular beads, which is predicted to providemultiple intersecting nodal rings in the ultrasonic regime. By unveiling theseyet unseen classical topological phases, we discuss the resilience of theassociated novel surface states that appear entirely unaffected to the type ofcrystal termination, making them a superb platform in ultrasonic devices fornon-destructive testing and material characterization.

Ultrasonic nodal chains in topological granular metamaterials