Doping-type-dependent pairing symmetry in predicted Ni-based high-$T_c$ superconductor La${}_2$Ni${}_2$Se${}_2$O${}_3$

We study the electronic instabilities of newly predicted Ni-based high-$T_c$ superconducting material La${}_2$Ni${}_2$Se${}_2$O${}_3$ based on the random phase approximation. Our calculations on the susceptibility indicate that the collinear antiferromagnetic state in the parental compound is induced by the perfect Fermi surface nesting. Our further calculations reveal that the ground states of the doped compound are the $s_{\pm }$- and $d_{xy}$-wave superconducting states driven by the antiferromagnetic spin fluctuations enhanced by the quasi-nestings. Interestingly, the $s$- and $d$-wave pairings occur in the hole and electron doping cases, respectively. This doping-type dependence of the pairing symmetry can be understood from the doping dependence of the nested Fermi pockets.