Boundary Gauge Field-Induced Topological Hinge States in Photonic Metamaterials

Higher-order topological insulators (HOTIs) can support boundary states at least two dimensions lower than the bulk, attracting intensive attention from both fundamental science and application sides. Lattice-based tight-binding models such as Benalcazar-Bernevig-Hughes model have driven significant advancements in realizing HOTIs across various physical systems. Here, beyond lattice model, we demonstrate that a cylinder with an arbitrary cross section, composed of a homogeneous electromagnetic medium featuring nontrivial second Chern numbers c2 = ±1 in a synthetic five-dimensional space, can exhibit topologically protected HOTI-type hinge states in three-dimensional laboratory space. Interestingly, this hinge state is essentially a chiral zero mode arising from the interaction between Weyl arc surface states, guaranteed by a nontrivial c2, and an effective magnetic field induced by the curvature of the cylinder surface. We experimentally realize such a cylinder using a photonic metamaterial and confirm the existence of hinge states via microwave near-field measurements. Our work introduces the concept of boundary gauge fields and establishes the link between synthetic-space c2 and real-space HOTI states, thereby generalizing HOTIs to corner-less systems.