Self-doped Molecular Mott Insulator for Bilayer High-Temperature Superconducting La3Ni2O7

TL;DR

The authors propose a self-doped molecular Mott insulator picture for bilayer La$_3$Ni$_2$O$_7$, where a two-orbital $e_g$ manifold forms bonding/antibonding states under interlayer coupling, and self-doping arises when the antibonding sector becomes partially occupied. They derive a two-orbital, renormalized $t$-$J$ (Kugel-Khomskii) description for the low-energy theory, with a Gutzwiller projection capturing strong correlations and a pairing tendency that depends on interorbital hybridization. Through exact diagonalization and renormalized mean-field calculations, they show that the system can support $d$-wave or extended $s$-wave superconductivity depending on the interorbital hopping $t^{xz}$, with Hund's coupling $J_H$ setting bounds on the molecular Mott regime. The work highlights how self-doping in a molecular Mott framework can account for high-temperature superconductivity in La$_3$Ni$_2$O$_7$, and it points to chemical hole doping and oxygen vacancies as practical levers to tune superconducting behavior.

Abstract

The bilayer structure of recently discovered high-temperature superconducting nickelates La$_3$Ni$_2$O$_7$ provides a new platform for investigating correlation and superconductivity. Starting from a bilayer Hubbard model, we show that there is a molecular Mott insulator limit formed by the bonding band owing to Hubbard interaction $U$ and large interlayer coupling. This molecular Mott insulator becomes self-doped due to electrons transferred to the antibonding bands at a weaker interlayer coupling strength. The self-doped molecular Mott insulator is similar to the doped Mott insulator studied in cuprates. We propose La$_3$Ni$_2$O$_7$ to be a self-doped molecular Mott insulator, whose molecular Mott limit is formed by two nearly degenerate antisymmetric $d_{x^2-y^2}$ and $d_{z^2}$ orbitals. Partial occupation of higher energy symmetric $d_{x^2-y^2}$ orbital leads to self-doping, which may be responsible for high-temperature superconductivity in La$_3$Ni$_2$O$_7$. The effects of Hund's coupling $J_H$ on the low-energy spectra are also studied via exact diagonalization. The proposed low-energy theory for La$_3$Ni$_2$O$_7$ is found to be valid in a wide range of $U$ and $J_H$.

Figures (6)

• Figure 1: Self-doped Molecular Mott insulator. (a1) and (b1) show bands formed by molecular bonding and anti-bonding orbitals that are separated by different values of the molecular orbital splitting $\eta$. (a2) and (b2) schematically show the upper and lower Hubbard band resulting from onsite repulsion $U$ in different limits of $\eta/U$. The filling considered here is one electron per molecule. For $\eta\gg U$ as shown in (a2), the four Hubbard bands are isolated from each other and the electrons will fill the lower bonding Hubbard band only. This corresponds to the scenario of a molecular Mott insulator. In the scenario of (b2) where $\eta< U$, overlap between the lower Hubbard bands of the two molecular orbitals is found due to small $\eta$. The two upper Hubbard bands at higher energy are empty and are not plotted here. At the quarter filling, the electrons now resides primarily in the lower Hubbard bonding band, with a small portion in the lower anti-bonding Hubbard band, giving rise to the self-doped molecular Mott insulator.
• Figure 2: Self-doped molecular Mott insulator from the bilayer Hubbard model. (a) schematic illustration of the bilayer Hubbard model with interlayer hopping is denoted by $\frac{\eta}{2}$, the intra-layer hopping $t$ and onsite repulsion $U$. The bonding and anti-bonding orbitals in the molecular basis is denoted by blue and red, respectively. The doublon state is denoted by purple. (b) Schematic energy dispersion of the bonding and the anti-bonding bands. At $\eta<W$, the ground state at the filling of one electron per molecule contains both the bonding and anti-bonding orbitals. (c) Schematic illustration of the self-doped molecular Mott insulator with large U. The blue and red circles denote the electrons in the bonding and the anti-bonding orbitals, respectively. Note the depicted doublon state with both orbitals occupied doesn’t cost U and is also allowed in the low energy range, see eq. \ref{['doublon']} in the text.
• Figure 3: Model for La$_3$Ni$_2$O$_7$ : two-orbital self-doped Molecular Mott insulator. (a) Local electronic orbitals of the interlayer pair $(\text{Ni}_2)^{5+}$. For each Ni atom, $3d$$t_{2g}$ are fully filled and not plotted here. With interlayer coupling $t_\perp^{x,z}$, the two sets of $e_g$ orbitals further split into four molecular orbitals. Two electrons occupy the $|z,+\rangle$ orbital which is much lower in energy than the other three orbitals. The remaining one electron predominantly occupies one of the two anti-bonding orbitals $|x,-\rangle_\sigma$ and $|z,-\rangle_\sigma$, with a small portion in the bonding orbital $|x,+\rangle_\sigma$, corresponding to the $\alpha$-band in the DFT calculation yaodx. (b) Schematic illustration of the self-doped Molecular Mott insulator. In the Mott limit, electrons can only occupy either one of the $|x,-\rangle_\sigma$ and $|z,-\rangle_\sigma$ orbitals due to the strong onsite Hubbard repulsion, as depicted in blue and green, respectively. A small amount of doublon states, namely $|x,-\rangle_\sigma \otimes|x,+\rangle_\sigma$ as depicted in blue-red circles, can exist due to no cost in U. With the total number of electrons fixed, formation of a doublon will generate a hole, leading to the self-doped molecular Mott insulator.
• Figure 4: Mean field results for the two-orbital self-doped molecular Mott insulator obtained with in-plane intra-orbital hopping $t^{xx}=1$, $t^{zz}=0.2$, and inter-orbital hopping $t^{xz}=0.1$ (a), $t^{xz}=0.6$ (b), plotted as a function of the self-doped hole density $n_h$. The Hubbard interaction is set as $U_A=6$. The figures from top to bottom show the results for the pairing component in the extended s-wave $\Delta_{s}$ and d-wave $\Delta_{d}$, channel, the hopping mean field $\chi$ and the occupation number $n_{x-}$, $n_{z-}$. With increasing interorbital hybridization $t^{xz}$, we find the pairing symmetry changes from $d$-wave to $s$-wave. We estimate from DFT calculations 2025Jiang$t^{xz}\approx0.4-0.6$ and self-doping $n_h\approx 0.17$ (area shaded in gray) corresponding to the $\alpha$-band.
• Figure 5: Local spectra and projected wave function components of the low-energy eigen states. (a) The spectra obtained under $t_\perp^z=-1\text{eV},\, t_\perp^x=0.2\text{eV},\, E_x=1.3\text{eV},\, J_H=0\text{eV}$. The dominant wave function components are plotted along the spectra of the three lowest energy eigenstates according to $|z,+\rangle_{\uparrow\downarrow} \otimes |x,-\rangle$ (blue), $|z,+\rangle_{\uparrow\downarrow} \otimes |z,-\rangle$ (green) and $|z,+\rangle_{\uparrow\downarrow} \otimes |x,+\rangle$ (yellow). The first two electronic configurations correspond to the two anti-symmetric orbitals forming the molecular Mott insulator, and the last one contributes to the self-doping effect. (b) The spectra obtained with $t_\perp^x=0.4\text{eV}$ in comparison to (a). The gap between the $|x,-\rangle$ and the $|x,+\rangle$ becomes larger, indicating a weaker self-doping effect. (c) The spectra obtained with $J_H=0.1U$ in comparison to (a). The two eigenstates with electrons occupying different orbitals have smaller slope in $U$ due to Hund’s coupling. Around $U=4eV$, the local electronic spectra contains two nearly degenerate anti-symmetric orbitals $|x,-\rangle$ and $|z,-\rangle$, with $|x,+\rangle$ above by $\sim t_\perp^x$. (d) The spectra obtained with $U=3$eV as a function of $J_H/U$. The molecular Mott insulating regime is valid below $J_H/U\sim0.25$. With larger $J_H/U$, the high spin states become energetically favored over the $|\psi_2\rangle$.