| Summary: | We demonstrate that the topological hinge state can possess a nontrivial interstate Berry curvature in the non-Abelian formulation of the Berry curvature. It can be readily probed by the circular photogalvanic effect (CPGE), with the light illuminating a specific hinge, and we refer to it as the hinge CPGE. As a concrete example, we calculate the hinge CPGE in ferromagnetic MnBi_{2n}Te_{3n+1}, and find that the hinge CPGE peak structure well reflects the interstate Berry curvature of hinge states and the optical sum rule captures the interstate Berry curvature between the hinge state and the ground state. Thus, the hinge CPGE provides a promising route towards the optical detection of a hinge-state geometrical structure.
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