Design of a higher-order nodal-line semimetal in a spring-shaped acoustic topological crystal

Abstract

The concept of higher-order topology has prompted the development of topological insulators, and a series of theoretical and experimental schemes have been proposed and realized to demonstrate higher-order hinge or corner states. While these ideas thrive in topological semimetals such as higher-order Dirac or Weyl semimetals, other degeneracy types such as nodal lines or nodal loop semimetals still remain to be fully exploited. In this work we consider a setup that hosts an acoustic springlike higher-order nodal-line semimetal protected by a screw-rotational symmetry. The underlying sandwich architecture is engineered with different coupling modes between different layers to construct a specific space group configuration, which enables the emergence of higher-order nodal lines in momentum space. Numerical calculations of the band dispersion show that nodal lines in opposite directions result in linked double hinge arcs. A corresponding topological invariant index is introduced to characterize the different topological phases. Furthermore, a propagation simulation of hinge and surface waves in a multilayer sample is performed that matches well with theoretical computations. Our work thus presents a higher-order nodal-line semimetal in an acoustic crystal and may receive practical applications in manufacturing sonic devices.