Electrons driven coherently by laser light can exhibit nonperturbative geometric effects. Drastic deformation and gap openings of the electrons' Floquet bands occur at one-photon resonances since the electron and hole bands hybridize through their replicas at the lowest-order photon exchange. We study the evolution of Floquet bands in three-dimensional (3D) materials driven by circularly polarized light (CPL) using the Dirac model. We find that the light-induced gap closes at a select few points in the momentum space where Floquet Weyl points are formed. The Weyl points are protected by their monopole charge and can merge, separate, or pair annihilate depending on the anisotropy of electrons and the ellipticity of the incident light. In isotropic 3D Dirac electrons driven by CPL, the Weyl points merge to form Floquet double-Weyl points with topological charge $\pm 2$. Our results reveal a universal aspect of light-matter interactions in 3D quantum materials and open a route towards controllable versatile electromagnetic responses associated with light-induced Floquet Weyl states.

• Received 23 October 2023
• Accepted 10 January 2024

DOI:https://doi.org/10.1103/PhysRevResearch.6.L012027

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Published by the American Physical Society