Theoretical study on the crystal structure of a bilayer nickel-oxychloride Sr$_3$Ni$_2$O$_5$Cl$_2$ and analysis on the occurrence of possible unconventional superconductivity

The discovery of superconductivity under high pressure with $T_c$ exceeding 80 K in a bilayer nickelate La$_3$Ni$_2$O$_7$ has led to a strong desire to realize similar high $T_c$ phenomena at ambient pressure. As one possible path toward realizing superconductivity at ambient pressure, we here propose to consider Sr$_3$Ni$_2$O$_5$Cl$_2$ as a possible candidate. In this study, we theoretically investigate the electronic structure of Sr$_3$Ni$_2$O$_5$Cl$_2$ and its structural stability. Our phonon calculation shows that this compound with the $I4/mmm$ tetragonal structure is dynamically stable even at ambient pressure. The characteristic crystal field in this compound lowers the Ni-$d_{3z^2-r^2}$ orbital energy, by which the Ni-$d_{3z^2-r^2}$ orbital becomes rather closer to the half-filling in Sr$_3$Ni$_2$O$_5$Cl$_2$ than La$_3$Ni$_2$O$_7$. As a result, we find that superconductivity is enhanced even though a relatively strong orbital hybridization between the $t_{2g}$ and $e_g$ orbitals is somewhat detrimental for superconductivity. We also check the formation enthalpy, which shows that the high-pressure synthesis can be a good way to actually produce Sr$_3$Ni$_2$O$_5$Cl$_2$. We find that Sr$_3$Ni$_2$O$_5$Cl$_2$ is a promising new candidate of bilayer-nickelate superconductors, which can possess even higher $T_c$ than pressurized La$_3$Ni$_2$O$_7$, at ambient pressure.