Intertwined Electron Pairing in the Bilayer Two-orbital Kanamori-Hubbard Model: a Unified Picture of Two Superconductivities in $\mathrm{La_3Ni_2O_7}$

Abstract

The mechanism of superconductivity in $\mathrm{La_3Ni_2O_7}$ bulk and film superconductors remains actively debated. Here, we investigate the bilayer two-orbital Kanamori-Hubbard model for $\mathrm{La_3Ni_2O_7}$ using cellular dynamical mean-field theory. We discover two intertwined $s_{\pm}-$ wave superconductivities with distinct physical origins. We show that when the $d_{z^2}$ orbital is under-doped, electron pairing associated to Hund's coupling $J_H$ prevails. As $d_{z^2}$ hole-doping $\delta_z$ increases, a second superconductivity, which is largely insensitive to $J_H$ but exhibiting a critical reliance on the $d_{z^2}$ - $d_{x^2-y^2}$ hybridization $V$, arises. These two primary pairing states exhibit comparable maximum transition temperatures $T_c$, and evolve from one to the other following a smooth $T_c$ versus $\delta_z$ relation. A stark particle-hole asymmetry is observed in the superconducting phase diagram, indicating the crucial role played by the $\gamma-$ band of $d_{z^2}$ orbital in pairing. Our results present a picture unifying the two possible pairing mechanisms in $\mathrm{La_3Ni_2O_7}$ superconductors. We discuss the implications of our findings to recent experiments.