Anomalous Hall Conductivity as an Effective Means of Tracking the Floquet Weyl Nodes in Quasi-One-Dimensional $\beta$-Bi${}_4$I${}_4$

Abstract

While Floquet engineering offers a powerful paradigm for manipulating topological phases, particularly Floquet Weyl semimetals, establishing an experimentally feasible strategy for tracking the dynamic evolution of such states remains a significant challenge. Here, we propose that the anomalous Hall effect (AHE), as a sensitive, all-electrical probe, can be used to track Floquet Weyl nodes. Using first-principles calculations and symmetry analysis on the quasi-one-dimensional material $\beta$-Bi${}_4$I${}_4$, we demonstrate that circularly polarized light breaks time-reversal symmetry, driving the system from a trivial insulator into a Floquet Weyl semimetal phase characterized by a nonzero Berry curvature flux. Crucially, by continuously tuning the polarization phase $\phi$ of the driving field, we show that the trajectory of the induced Weyl nodes is highly controllable, leading to their migration and eventual annihilation at high-symmetry points. We reveal that the anomalous Hall conductivity maps directly onto this topological evolution, serving as a definitive fingerprint for the generation and dynamics of Weyl nodes.