  Persistent spin texture (PST), a property of solid-state materials
maintaining unidirectional spin polarization in the momentum $k$-space, offers
a route to deliver the necessary long carrier spin lifetimes through the
persistent spin helix (PSH) mechanism. However, most of the discovered PST
locally occurred in the small part around certain high symmetry $k$-points or
lines in the first Brillouin zone (FBZ), thus limiting the stability of the PSH
state. Herein, by symmetry analysis and first-principles calculations, we
report the emergence of full-zone PST (FZPST), a phenomenon displaying the PST
in the whole FBZ, in the two-dimensional group IV-V $A_{2}B_{2}$ ($A$ = Si, Sn,
Ge; $B$ = Bi, Sb) compounds. Due to the existence of the in-plane mirror
symmetry operation in the wave vector point group symmetry for the arbitrary
$\vec{k}$ in the whole FBZ, fully out-of-plane spin polarization is observed in
the $k$-space, thus maintaining the FZPST. Importantly, we observed giant spin
splitting in which the PST sustains, supporting large SOC parameters and small
wavelengths of the PSH states. Our $\vec{k}\cdot\vec{p}$ analysis demonstrated
that the FZPST is robust for the non-degenerate bands, which can be effectively
controlled by the application of an external electric field, thus offering a
promising platform for future spintronic applications.
