Quantum mechanics

Gapless playback

Surface states

Economics

Classical mechanics

Band gap

Surface (topology)

Position and momentum space

Physics

Topological order

Mathematics

Topological insulator

Semimetal

Condensed matter physics

Geometry

Quantum

Combinatorics

Finance

Topology (electrical circuits)

Order (exchange)

Weyl semimetal

Hinge

Nature Materials

The notion of higher-order topological insulators has endowed materials with topological states beyond the first order. Particularly, a three-dimensional (3D) higher-order topological insulator can host topologically protected 1D hinge states, referred to as the second-order topological insulator, or 0D corner states, referred to as the third-order topological insulator. Similarly, a 3D higher-order topological semimetal can be envisaged if it hosts states on the 1D hinges. Here we report the realization of a second-order topological Weyl semimetal in a 3D-printed acoustic crystal, which possesses Weyl points in 3D momentum space, 2D Fermi arc states on surfaces and 1D gapless states on hinges. Like the arc surface states, the hinge states also connect the projections of the Weyl points. Our experimental results evidence the existence of the higher-order topological semimetal, which may pave the way towards innovative acoustic devices.

Higher-order topological semimetal in acoustic crystals