Floquet-Weyl semimetals (FWSMs) generated by irradiation of a continuous-wave laser with left-hand circular polarization (rotating in counterclockwise sense with time) on the group II–V narrow-gap semiconductor ${\mathrm{Zn}}_3{\mathrm{As}}_2$ are theoretically investigated, where the frequency of the laser is set nearly resonant with the band gap of the crystal. It is found that the excitation of the crystal by such a laser induces two types of FWSM phases that differ absolutely in character. To be specific, the associated two pairs of Weyl points are stably formed by band touching between Floquet sidebands ascribable to a valence band labeled $J_z=\pm 3/2$ and a conduction band labeled $J_z=\pm 1/2$, where $J_z$ represents the $z$ component of total angular-momentum quantum number of the $\mathrm{\Gamma }$ point and a double sign corresponds. Here, one FWSM state composed of the up-spin Floquet sidebands relevant to $J_z=3/2$ and $1/2$ shows almost quadratic band-touching in the vicinity of the associated pair of Weyl points, while the other FWSM state composed of the down-spin Floquet sidebands relevant to $J_z=-3/2$ and $-1/2$ shows linear band-touching. Furthermore, it is revealed that both up-spin and down-spin sidebands host nontrivial two-dimensional surface states that are pinned to the respective pairs of the Weyl points. Both surface states also show different energy dispersions and physical properties. A more detailed discussion is presented in the text on the origin of the above findings, the chirality of the FWSM phases, the alteration of topological order, laser-induced magnetic properties, and so on.

• Received 30 December 2021
• Revised 24 May 2022
• Accepted 9 August 2022

DOI:https://doi.org/10.1103/PhysRevB.106.085206