  The new two-dimensional materials, MoSi$_2$N$_4$ and WSi$_2$N$_4$ are
experimentally synthesized successfully and various similar structures are
predicted theoretically. Here, we report the electronic properties with a
special focus on the band splitting in WA$_2$Z$_4$ (A=Si, Ge; Z=N, P, As),
using state-of-the-art density functional theory and many-body perturbation
theory (within the framework of G$_0$W$_0$ and BSE). Due to the broken
inversion symmetry and strong spin-orbit coupling effects, we detect coupled
spin-valley effects at the corners of the first Brillouin zone (BZ).
Additionally, we observe cubically and linearly split bands around the $\Gamma$
and M points, respectively. Interestingly, the in-plane mirror symmetry
($\sigma_h$) and the reduced symmetry of arbitrary $k$-point, enforce the
persistent spin textures (PST) to occur in full BZ. We induce the Rashba
splitting by breaking the $\sigma_h$ through an out-of-plane external electric
field (EEF). The inversion asymmetric site point group of the W atom introduces
the hidden spin polarization in centrosymmetric layered bulk counterparts.
Therefore, the spin-layer locking effect, namely, energy degenerate opposite
spins spatially segregated in the top and bottom W layers, has been identified.
Our low energy $k.p$ model demonstrates that the PST along the M-K line is
robust to EEF and layer thickness, making them suitable for applications in
spintronics and valleytronics.
