Higher-order Weyl semimetals on nonorientable manifolds

Higher-order Weyl semimetals (HOWSMs), characterized by the coexistence of two-dimensional Fermi arc surface states and one-dimensional topological hinge states, establish the fundamental connection between Weyl physics and higher-order topology. However, previous studies have exclusively focused on HOWSMs within orientable manifolds. Here, we report the realization of HOWSMs on nonorientable manifolds through the introduction of Z2 gauge fields. The key feature is that the Fermi arc surface states and higher-order hinge states coexist within identical kz topological regions, which is fundamentally distinct from conventional HOWSMs. At last, we propose an experimental scheme based on acoustic resonator arrays, which may stimulate similar research works in other systems such as circuit, photonic, and cold-atom systems. Our work highlights the subtle yet crucial interplay between HOWSMs and their underlying manifolds.