  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 Zn$_3$As$_2$ are
theoretically investigated, where the frequency of the laser is set nearly {\it
resonant} with a band gap of the crystal. It is found that the excitation of
the crystal by such a laser induce two types of FWSM phases that differ
absolutely in characters. 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 as $J_z=\pm3/2$ and a conduction band labeled as
$J_z=\pm 1/2$, where $J_z$ represents the $z$-component of total angular
momentum quantum number of $\Gamma$-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. Further, 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. More detailed discussion is made in
the text on the origin of the above findings, chirality of the FWSM phases,
alteration of topological order, laser-induced magnetic properties, and so on.
