Topological acoustics with orbital-dependent gauge fields

The synthetic gauge field, projectively enriching the algebraic structure of spatial symmetries, has become a hotspot in topological physics recently. The intrinsic orbital degrees of freedom, playing a fundamental role in solid-state materials and offering an alternative platform, have not yet been studied extensively in classical wave systems, such as acoustic systems. Here we propose orbital-dependent gauge fields by utilizing the intrinsic degenerate p orbitals in a square lattice of coupled acoustic cavities. To realize the orbital-related synthetic gauge fields, an acoustic disk-shaped resonator hosting degenerate p orbitals is designed, where the signs of transverse and longitudinal hoppings can be simultaneously tailored on demand by tuning the geometries of coupling waveguides in the dimer units. We then show two different types of orbital-dependent topological insulators resting with the orbital-dependent gauge fields via the tight-binding method and full-wave simulation. Moreover, an orbital-dependent semimetal phase is revealed in the square lattice with a varied dimerization pattern. Our findings reveal the existence of abundant physical phenomena as the cavity orbitals and gauge fields meet with the topology, initializing the framework for orbital-related topological physics and opening up opportunities for potential multifunctional acoustic applications, such as sound sensing and trapping.