Floquet Gauge Anomaly Inflow and Arbitrary Fractional Charge in Periodically Driven Topological-Normal Insulator Heterostructures

Usually, when coupling in a background gauge field, topological zero modes would yield an anomalous current at the interface, culminating in the zero-mode anomaly inflow, which is ultimately conserved by extra contributions from the topological bulk. However, the anomaly inflow mechanism for guiding Floquet steady states is rarely explored in periodically driven systems. Here we synthesize a driven topological-normal insulator heterostructure and propose a Floquet gauge anomaly inflow, associated with the occurrence of arbitrary fractional charge. Through our photonic modeling, we experimentally observed a Floquet gauge anomaly as the system was driven into anomalous topological phases. Prospectively, we believe our findings could pave a novel avenue on exploring Floquet gauge anomalies in driven systems of condensed matter, photonics, and ultracold atoms.

Figure 1

Anomaly inflow on a domain wall in static and periodically driven $\mathrm{TI}/\mathrm{NI}$ heterostructures. (a) The domain wall construction for zero-mode anomalies in the presence of a background gauge field $\mathit{A}$. The topological excitation holds a ½ fractional charge. (b) The anomalous domain wall construction for the $\pi$-mode anomaly. The anomalous topological excitation holds a ½ fractional charge. (c) A generalized Floquet-gauge-induced $\pi$-mode domain wall construction. The Floquet gauge for the two sides is relatively shifted by $T/f$. The fractional charge is $Q_{\pi }=1/f$.

Figure 2

The quasienergy spectrum and the $\pi$-mode eigenstate evolution from Floquet-Bloch theorem. (a) The emergence of the $\pi$-mode domain wall in the quasienergy spectrum. (b) The “open-close-open” mechanism of the topological $\pi$ gap in quasi-energy-momentum space. At the driven frequencies $\omega /\mathrm{\Delta }=1/3$,1, the $\pi$ gap is closed nontrivially, with $\mathrm{\Delta }$ being the bandwidth. (c) The quasienergy evolution of the $\pi$-mode eigenstate at the interface.

Figure 3

The confinement signature of Floquet gauge anomaly with arbitrary fractional charges in driven systems. (a)–(e) Time evolutions with fractional charge of $Q_{\pi }=1/2$, $1/3$, $1/5$, $1/7$, and $1/17$, respectively, are presented, respectively, from left to right. The fractional charge is topologically induced by the spatial change of the Floquet gauge. Topological excitations with smaller charges are more weakly confined.

Figure 4

Experimental observation of the Floquet $\pi$-mode anomaly ranging from the adiabatic limit to the high-frequency limit. (a) The reading system for detecting the output intensity distribution of the photonic modeling of driven $\mathrm{TI}/\mathrm{NI}$ heterostructures. The designed structures (b)–(d), simulated propagation dynamics (e)–(g), and experimental measurements of the output intensity distributions (h)–(j) are shown. The $\pi$-mode anomaly appears only at the intermediate frequency range (c),(f),(i).