Theoretical proposal of superconductivity in hole-doped reduced bilayer nickelate La3Ni2O6: a manifestation of orbital-space bilayer model with incipient bands

Abstract

A correspondence exists between the multi-orbital Hubbard model and the bilayer Hubbard model, in which superconductivity is optimized in an incipient-band regime in both cases. In the multi-orbital system, the orbital level offset $ΔE$ plays a role analogous to the interlayer hopping in bilayer systems, and superconductivity is enhanced for large $ΔE$. We refer to such a multi-orbital model as an orbital-space bilayer model (OSBM). In this study, we theoretically propose that a reduced bilayer nickelate La$_3$Ni$_2$O$_6$ can be a candidate for a superconductor described by OSBM when an appropriate amount of holes is doped. By constructing a tight-binding model based on first-principles calculations, a large $ΔE$ between the Ni $d_{x^2-y^2}$ and the other $d$ orbitals is obtained due to the absence of outer apical oxygens. Furthermore, our fluctuation exchange approximation calculations indicate the emergence of $s\pm$-wave superconductivity driven by interorbital interactions in an incipient-band situation, where the superconducting gap function changes its sign between the $d_{x^2-y^2}$ and other $d$ orbital bands. We also investigate the energetic and dynamical stability of the crystal structure under atomic substitution and pressure. Although La$_3$Ni$_2$O$_7$ and La$_3$Ni$_2$O$_6$ share a similar chemical formula, our study shows that an entirely different pairing mechanism can take place in the latter.

Figures (10)

• Figure 1: Schematics of the Real-Space Bilayer Model (RSBM) and the Orbital-Space Bilayer Model (OSBM). The interlayer hopping $t_\perp$ in the RSBM gives rise to bonding and antibonding bands with an energy separation of $2t_\perp$. In the OSBM, orbital-level offsets $\Delta E$ between multiple orbitals play an analogous role. In both models, superconductivity is optimized in the incipient-band regime, where one band intersects the Fermi level while the other touches or lies slightly away from it. The correspondence between the RSBM and the OSBM has been established not only in a two-orbital model but also in multi-orbital systems, such as the five-orbital model.
• Figure 2: The crystal structure of La3Ni2O6. (a) and (b) indicate the $T$- and $T'$-type structures, respectively.
• Figure 3: The band structures of La3Ni2O6 in (a)--(c) the $T$-type and (d)--(f) the $T'$-type structure. The band dispersion of the five-orbital model is superposed to the first-principles bands.
• Figure 4: (a) The eigenvalues $\lambda$ of the linearized Eliashberg equation as a function of the band filling $n$ (the number of electrons per Ni atom), where $n=8.5$ corresponds to the stoichiometric case. The blue (red) lines are for the $T$ ($T'$) structure, and the dashed (solid) lines with squares (circles) represent the values obtained from the GGA (GGA$+U$) band structures, respectively. (b) Gap function obtained from the GGA$+U$ bands of the $T'$ structure ($n=8.1$). (c) Orbital occupations as functions of the Ni $d$ orbital filling. The "lower band" represents the average occupation of the $d_{3z^2-r^2}$, $d_{xz/yz}$, and $d_{xy}$ orbitals. (d) The filling dependence of the chemical potential $\mu$. Black dashed lines indicate the level of the chemical potential $\mu$ for each band filling from 8.1 to 8.5. We set the value of $\mu$ at $n=8.5$ to zero. (e) Schematics of the realization of incipient bands by hole doping.
• Figure 5: (a) Filling dependence of the eigenvalue $\lambda$ of the Eliashberg equation when the interorbital interactions. In addition to the calculations with the interaction parameters obtained from cRPA (denoted as "original"), results are also shown for (i) $U'=J=J'=0$ for all orbitals and (ii) $U'=J=J'=0$ between $e_g$ and $t_{2g}$ orbitals. (b) Relationship between the orbitals at each Ni site in La3Ni2O6 and the OSBM and RSBM. Within the present model and analysis, the OSBM contribution dominates over that of the RSBM (see the text for details).