Observation of Dirac hierarchy in three-dimensional acoustic topological insulators

Abstract

Dirac cones (DCs) play a pivotal role in various unique phenomena ranging from massless electrons in graphene to robust surface states in topological insulators (TIs). Recent studies have theoretically revealed a full Dirac hierarchy comprising an eightfold bulk DC, a fourfold surface DC, and a twofold hinge DC, associated with a hierarchy of topological phases including first-order to third-order three-dimensional (3D) topological insulators, using the same 3D base lattice. Here, we report the first experimental observation of the Dirac hierarchy in 3D acoustic TIs. Using acoustic measurements, we unambiguously reveal that lifting of multifold DCs in each hierarchy can induce two-dimensional (2D) topological surface states with a fourfold DC in a first-order 3D TI, one-dimensional (1D) topological hinge states with a twofold DC in a second-order 3D TI, and zero-dimensional (0D) topological corner states in a third-order 3D TI. Our work not only expands the fundamental research scope of Dirac physics, but also opens up a new route for multidimensional robust wave manipulation.

References in corpus (10)

• The electronic properties of graphene
• Many-Body Physics with Ultracold Gases
• Topological Photonics
• Scheme to Achieve Silicon Topological Photonics
• Observing Zitterbewegung for photons near the Dirac point of a two-dimensional photonic crystal
• Acoustic realization of quadrupole topological insulators
• Three dimensional photonic Dirac points in metamaterials
• Projectively enriched symmetry and topology in acoustic crystals
• Higher-order Dirac Semimetal in a Photonic Crystal
• Experimental observation of non-Abelian earring nodal links in phononic crystals

Cited by in corpus (3)

• Higher-order topological phases in crystalline and non-crystalline systems: a review
• Monopole topological resonators
• Tunable two-dimensional Dirac-Weyl semimetal phase induced by altermagnetism