Topotactical hydrogen induced single-band $d$-wave superconductivity in La$_2$NiO$_4$

Abstract: La$2$NiO$_4$ is an antiferromagnetic insulator with a structural resemblance to its cuprate counterpart, La$_2$CuO$_4$. However, La$_2$CuO$_4$ has a Cu$^{2+}$ or 3$d^9$ electronic configuration that needs to be hole or electron doped for superconductivity, whereas La$_2$NiO$_4$ is 3$d^8$ with divalent Ni$^{2+}$. Making a cuprate analog through conventional electron doping is impractical due to the rarity of trivalent substituents for La. In this work, we propose an alternative route: intercalating topotactical hydrogen which is possible through electric-field-controlled protonation and transforms La$_2$NiO$_4$ into a 3$d{x^2-y^2}$ single-band two-dimensional anti-ferromagnetic Mott insulator analogous to La$_2$CuO$_4$. This we find through density-functional theory and dynamical mean-field theory calculations. The furthergoing dynamical vertex approximation predicts that H-La$_2$NiO$_4$ can host $d$-wave superconductivity under 15\% hole doping with a critical temperature above 20\,K. Our findings not only suggest a new method for tuning the electronic structure of layered nickelates but also provides theoretical evidence for a new nickelate superconductor, awaiting experimental synthesis.