Anomalous Hall effect of light-driven three-dimensional Dirac electrons in bismuth

Recent advancement in laser technology has opened the path toward the manipulation of functionalities in quantum materials by intense coherent light. Here, we study three-dimensional (3D) Dirac electrons driven by circularly polarized light (CPL), when the photon energy lies within the Dirac bands. As an experimental realization of this setup, we irradiate a thin film sample of elemental bismuth, which is a well-known semimetal hosting 3D Dirac electrons, with mid-infrared CPL. We successfully observe the emergence of the anomalous Hall effect (AHE) via terahertz Faraday rotation that is both pump-helicity-dependent and instantaneous. We compare our experimental findings with the results of Floquet theory, which is a powerful framework for analyzing the electronic band structure driven by coherent light. The contribution from the band structures near the one-photon resonant positions to the AHE shows a field-strength dependence consistent with our experimental results. The effective Hamiltonian on which we base our model calculations also implies that a pair of "double Weyl points" emerge due to the CPL-induced hybridization between the occupied and unoccupied 3D Dirac bands. Our findings shed light on ultrafast control of material properties in nonlinear topological optics.