Theoretical study on the possibility of high $T_c$ s$\pm$-wave superconductivity in the heavily hole-doped infinite layer nickelates

We theoretically propose a possibility of realizing high $T_c$ superconductivity having $s\pm$-wave symmetry in the heavily hole-doped infinite layer nickelates La${}_{1-x}$Sr${}_x$NiO${}_2$. We consider situations where the original $P4\mathrm{/}mmm$ symmetry of LaNiO${}_2$ is maintained even for a significant amount of Sr substitution by growing thin films on substrates having tetragonal symmetry. Considering such cases is indeed justified by our phonon calculations. For electron configurations somewhat close to $d^8$, the interaction between the $d_{x^2-y^2}$ band and the other $3d$ bands that lie just below the Fermi level results in an enhancement of superconductivity where the sign of the gap function is reversed between the former and the latter bands. The strong enhancement of superconductivity can be attributed to the large energy level offset between $d_{x^2-y^2}$ and other orbitals due to the absence of the apical oxygens, as has been pointed out in previous studies.