# Ultrasonic nodal chains in topological granular metamaterials

## TL;DR

This paper introduces a 3D granular metamaterial that exhibits ultrasonic nodal chains, revealing new classical topological phases with robust surface states suitable for ultrasonic testing and material analysis.

## Contribution

The study demonstrates a novel 3D mechanical metamaterial with multiple intersecting nodal rings, advancing topological phases in classical systems and overcoming challenges faced in electronic topological materials.

## Key findings

- Unveiled ultrasonic nodal chains in granular metamaterials
- Surface states are unaffected by crystal termination
- Potential applications in ultrasonic non-destructive testing

## 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, detrimental effects of the spin-orbit interaction, along with the merging of the underlying surface states into the bulk pose great challenges for growing advancements, but fortunately enable other systems, such as bosonic lattices, as ideal platforms to overcome these obstacles. Here we demonstrate a 3D mechanical metamaterial made of granular beads, which is predicted to provide 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 superb platform in ultrasonic devices for non-destructive testing and material characterization.