Tunable antichiral hinge state in photonic synthetic dimensions

Recent research in two-dimensional topological matter has generalized the notion of edge states from chiral to antichiral configurations with the same propagating direction at parallel edges, revealing a rich variety of robust transport phenomena. Here we propose that antichiral hinge states can emerge in a three-dimensional higher-order topological insulator or semimetal, where two surface or bulk Dirac points are connected by the hinge states. The band dispersion can be controlled and tilted independently for each hinge using properly designed tunnelings, resulting in tunable antichiral hinge states with programmable propagation direction and velocity. Moreover, we propose experimental realization schemes based on a one-dimensional coupled cavity array with additional synthetic dimensions represented by the photonic orbital angular momentum and frequency. We introduce both longitudinal and transversal electro-optic modulators to generate the desired tunable tunnelings along the synthetic dimensions, which significantly reduce the experimental complexity by eliminating the need for beam splittings and auxiliary cavities. The tunable antichiral hinge states are confirmed by the photonic transmission spectra. Our work presents robust and tunable antichiral hinge-state transports, which pave the way for exploring novel topological matter and their device applications.