  We use relativistic ab-initio methods combined with model Hamiltonian
approaches to analyze the normal-phase electronic and structural properties of
the recently discovered WP superconductor. Remarkably, the outcomes of such
study can be employed to set fundamental connections among WP and the CrAs and
MnP superconductors belonging to the same space group. One of the key features
of the resulting electronic structure is represented by the occurrence of
multiple band crossings along specific high symmetry lines of the Brilloiun
zone. In particular, we demonstrate that the eight-fold band degeneracy
obtained along the SR path at (kx,ky)=(Pi,Pi) is due to inversion-time reversal
invariance and a pair of nonsymmorphic symmetries. The presence of multiple
degenerate Fermi points along the SR direction constraints the topology of the
Fermi surface, which manifests distinctive marks when considering its evolution
upon band filling variation. If the Fermi level crosses the bands along the SR
line as it happens at the nominal filling of the MnP, these Fermi surfaces are
open or closed Fermi pockets. Moving the relative position of the Fermi level
away from the eight-fold degenerate bands as for the WP and CrAs compounds, the
electronic changeover exhibits a simultaneous modification of the Fermi surface
dimensionality and topology. Four two-dimensional (2D) Fermi surface sheets are
centered around the SR line with a corrugated profile along the kz direction.
Moreover, we show that the spin-orbit interaction determines a selective
removal of the band degeneracy and, consequently, a splitting of the quasi 2D
Fermi sheets, as it happens in WP. Finally, we comment on the connections
between our results and recent experimental and theoretical proposals about the
triplet superconductivity in this class of compounds.
