Multiple band crossings and Fermi surface topology: Role of double nonsymmorphic symmetries in MnP-type crystal structures

Abstract

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 Brillouin zone. In particular, we demonstrate that the eightfold band degeneracy obtained along the $\mathit{SR}$ path at $({k}_{x},{k}_{y})=(\ensuremath{\pi},\ensuremath{\pi})$ is due to inversion time-reversal invariance and a pair of nonsymmorphic symmetries. The presence of multiple degenerate Fermi points along the $\mathit{SR}$ direction constrains 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 $\mathit{SR}$ 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 eightfold 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 $\mathit{SR}$ line with a corrugated profile along the ${k}_{z}$ 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.