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.

中文翻译：

---

三维山谷对比声音


自旋和谷是晶体中电子的两个基本性质。几十年前在二维 （2D） 材料（如石墨烯）中建立的谷对比物理学中，它们之间的相似性得到了很好的理解——在反转对称性被打破的情况下，石墨烯中的两个谷表现出相反的轨道磁矩，类似于电子的自旋 1/2 行为，并且相反的 Berry 曲率导致半拓扑电荷。然而，谷对比物理学从未在 3D 晶体中被探索过。在这里，我们开发了一种 3D 声学晶体，展示了 3D 谷对比物理学。与基本二进制的自旋不同，3D 中的谷值可以取六个不同的值，每个值都带有一个不同方向的涡旋。拓扑谷输运从 2D 材料的边缘状态推广到 3D 材料的表面状态，具有有趣的特征，包括稳健传播、拓扑折射和谷腔定位。我们的结果为 3D 空间中的波浪操纵开辟了一条新的途径。