The spinless s-orbital diamond lattice model is a natural generalization of the graphene lattice to three dimensions. In this talk, I will show that many celebrated phenomena in graphene can find their three-dimensional counterparts in the diamond lattice. Using coupled acoustic cavity structures, we experimentally demonstrated several topological phases in artificial diamond lattices, including (1) three-dimensional flat Landau levels induced by artificial gauge fields. These Landau levels are similar to those in strained graphene; (2) a third-order topological insulator from coupling dimerization, which is an extension of the second-order topological insulator in anisotropic graphene; and (3) a three-dimensional valley-Hall phase induced by a staggered on-site potential, which hosts an intriguing vectorial valley contrasting physics beyond the conventional binary valley physics in graphene. These topological phases exhibit novel localization and transport behaviors with topological protection, and are promising for robust wave control in three dimensions.

Please contact phweb@ust.hk should you have questions about the talk.