Possible Superconductivity in Electron-doped Chromium Pnictide LaOCrAs

We constructed an effective tight-binding model with five Cr $3d$ orbitals for LaOCrAs according to first-principles calculations. Basing on this model, we investigated possible superconductivity induced by correlations in doped LaOCrAs using the functional renormalization group (FRG). We find that there are two domes of superconductivity in electron-doped LaOCrAs. With increasing electron doping, the ground state of the system evolves from G-type antiferromagnetism in the parent compound to an incipient $s_\pm$-wave superconducting phase dominated by electron bands derived from the $d_{3z^2-r^2}$ orbital as the filling is above $4.2$ electrons per site on the $d$-orbitals of Cr. The gap function has strong octet anisotropy on the Fermi pocket around the zone center and diminishes on the other pockets. In electron over-doped LaOCrAs, the system develops $d_{x^2-y^2}$-wave superconducting phase and the active band derives from the $d_{xy}$ orbital. Inbetween the two superconducting domes, a time-reversal symmetry breaking $s+id$ SC phase is likely to occur. We also find $s_\pm$-wave superconducting phase in the hole-doped case.