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

TL;DR

This paper proposes using the anomalous Hall effect as an electrical method to track the creation and movement of Floquet Weyl nodes in a driven topological material, demonstrated through first-principles calculations.

Contribution

It introduces a practical approach to monitor Floquet Weyl nodes via anomalous Hall conductivity, linking topological evolution to measurable electrical signals.

Findings

Circularly polarized light induces Floquet Weyl semimetal phase in $eta$-Bi$_4$I$_4$.

Tuning polarization phase controls Weyl node trajectories and annihilation.

Anomalous Hall conductivity directly reflects the topological evolution of Weyl nodes.

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 $\varphi$ 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.