Topological dual-Wannier cycles in orbital phononic crystals

Without external influences, electrons within an atom typically reside in the ground state, characterized by the lowest possible values of the principal and orbital angular momentum quantum numbers, 1 and 0, respectively. Recent studies have shown that the introduction of gauge flux into an artificial crystal plaquette can induce topological Wannier cycles originating from $1s$-like orbitals. However, the exploration of topological Wannier cycles involving complex orbits remains an open question. In this work, we experimentally realize topological dual-Wannier cycles, driven by the insertion of gauge flux into an orbital phononic crystal. This phononic crystal comprises disk-shaped acoustic cavities connected by pairs of parallel tubes, supporting $2s$-, $3p$-, and $4d$-like orbitals. The insertion of gauge flux is achieved by introducing a step screw dislocation, which induces cyclic spectral flows that bridge higher-order topological band gaps. By combining the orbital degree of freedom, these cyclic spectral flows give rise to dual-topological boundary states localized at the dislocation core. Our findings not only deepen the understanding of artificial gauge flux but also open new avenues for exploring orbital-related phenomena in classical wave systems.