Three-dimensional valley-contrasting sound

Abstract

Spin and valley are two fundamental properties of electrons in crystals. The similarity between them is well understood in valley-contrasting physics established decades ago in two-dimensional (2D) materials like graphene--with broken inversion symmetry, the two valleys in graphene exhibit opposite orbital magnetic moments, similar to the spin-1/2 behaviors of electrons, and opposite Berry curvature that leads to a half topological charge. However, valley-contrasting physics has never been explored in 3D crystals. Here, we develop a 3D acoustic crystal exhibiting 3D valley-contrasting physics. Unlike spin that is fundamentally binary, valley in 3D can take six different values, each carrying a vortex in a distinct direction. The topological valley transport is generalized from the edge states of 2D materials to the surface states of 3D materials, with interesting features including robust propagation, topological refraction, and valley-cavity localization. Our results open a new route for wave manipulation in 3D space.

8 pages, 5 figures

References in corpus (9)

• The Valley Hall Effect in MoS2 Transistors
• Valley Dependent Optoelectronics from Inversion Symmetry Breaking
• Observation of topological valley transport of sound in sonic crystals
• Topological nodal line semimetals
• Detecting Topological Currents in Graphene Superlattices
• Topological acoustics
• Valley Vortex States in Sonic Crystals
• Realization of an acoustic third-order topological insulator
• Strain-induced Landau Levels in arbitrary dimensions with an exact spectrum