Pairing without ${\hat{I}}^3$-Pocket in the La${}_3$Ni${}_2$O${}_7$ Thin Film

Abstract

The recent discovery of high-temperature superconductivity (HTSC) in the La${}_3$Ni${}_2$O${}_7$ ultrathin film at ambient pressure has aroused great research interest. The ${\hat{I}}^3$-pocket formed by the bonding $d_{z^2}$ band, which was previously proposed to be crucial in the pairing mechanism of pressurized bulk La${}_3$Ni${}_2$O${}_7$, is reported to be either present or absent here by different experimental groups, giving rise to the problem: what is the pairing mechanism and pairing nature without the ${\hat{I}}^3$-pocket? Here, we start from a band structure obtained via density-functional-theoretical calculation, which exhibits no ${\hat{I}}^3$-pocket. Then, equipped with electron interactions, we study the pairing nature via combined weak- and strong- coupling approaches, which provide consistent results. In the weak-coupling study, the nesting between the $\hat{I}\pm$- and ${\hat{I}}^2$- pockets leads to an $s^{\pm }$-wave pairing in which the gap signs on the two pockets are opposite, as provided by our random-phase-approximation based calculations. In real-space, the pairing pattern is dominated by the interlayer pairing of the $d_{x^2-y^2}$ orbital. In the strong-coupling study, as the $d_{z^2}$ orbitals are nearly half-filled and hence localized, the $d_{x^2-y^2}$ orbitals carry the HTSC. Driven by the interlayer superexchange transferred from the $d_{z^2}$ orbital through the Hund's rule coupling, the $d_{x^2-y^2}$ orbital electrons form interlayer $s$-wave pairing, as suggested by our slave-boson-mean-field study on the related two-orbital $t$-$J$ model. Projected onto the Fermi surface, this pairing just gives the $s^{\pm }$-wave pattern consistent with that obtained in the weak-coupling study. Our result is consistent with that obtained in recent scanning tunneling microscopy experiment.