Symmetry-enforced gapless surface states in three-dimensional acoustic gyroid structures

Abstract

The discovery of topological gapless phases challenges the perception that topological features necessarily require a bandgap, expanding the understanding of topological phases of matter in various realms including electric, photonic, and phononic systems. The progress on 3D topological gapless states in elastic and acoustic systems is still in its early stages of formulation and design. We here investigate 3D acoustic gyroid crystals supporting symmetry-enforced gapless surface states in minimal surface-based structures. The inherent chirality and morphology of gyroid surfaces enable the implementation of 3D acoustic crystals hosting symmetry-enforced Dirac points and topologically gapless surface states. The associated fourfold degeneracy is protected by the nonsymmorphic space group featuring a combination of screw symmetry and glide reflections. The presence of gapless surface arcs relies on band structure calculations conducted using finite element simulations, while preliminary experimental results on additively manufactured samples validate their occurrence in the proposed gyroid surfaces. With the continuous development in additive manufacturing techniques, the presented surface-based framework provides a platform to explore a variety of topological wave physics phenomena in 3D load-bearing, continuum materials of potential engineering relevance, among which superior acoustic absorption may be particularly promising.