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We constructed an effective tight-binding model with five Cr $3d$ orbitalsfor LaOCrAs according to first-principles calculations. Basing on this model,we investigated possible superconductivity induced by correlations in dopedLaOCrAs using the functional renormalization group (FRG). We find that thereare two domes of superconductivity in electron-doped LaOCrAs. With increasingelectron doping, the ground state of the system evolves from G-typeantiferromagnetism in the parent compound to an incipient $s_\pm$-wavesuperconducting 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 Fermipocket around the zone center and diminishes on the other pockets. In electronover-doped LaOCrAs, the system develops $d_{x^2-y^2}$-wave superconductingphase and the active band derives from the $d_{xy}$ orbital. Inbetween the twosuperconducting domes, a time-reversal symmetry breaking $s+id$ SC phase islikely to occur. We also find $s_\pm$-wave superconducting phase in thehole-doped case.

Possible Superconductivity in Electron-doped Chromium Pnictide LaOCrAs