Signatures of the $\pi$-mode anomaly in (1+1) dimensional periodically-driven topological/normal insulator heterostructures

Akin to zero-mode anomalies, such as the chiral anomaly of edge states in quantum Hall effect, in this work, a pi-mode anomaly is proposed in a 1+1 dimensional periodically-driven topological/normal insulator (TI/NI) heterostructure. Usually, when coupling in a background gauge field, the zero modes on domain walls would provide an anomalous current term that is eventually canceled by additional boundary contributions from the topological bulk, via the Callan-Harvey mechanism. This anomaly cancellation associated with the generalization of bulk-boundary correspondence is called anomaly inflow. Through our photonic modeling and setup of the Floquet TI/NI heterostructure, for the first time, we experimentally observed the $\pi$-mode domain wall in certain driven frequencies, which is always attached to the reminiscent Floquet gauge that plays the vital role of an emergent background field. Indeed, due to the possible emergence of Floquet gauge anomaly from the driven topological bulk, the resultant $\pi$-mode anomaly can be matched on the driven interface between Floquet domains. Prospectively, we believe our prediction and observation could pave a new avenue on exploring anomalies in both periodically-driven classical and quantum systems.