Pairing mechanism and superconductivity in pressurized La$_5$Ni$_3$O$_{11}$

Abstract

The discovery of superconductivity (SC) with critical temperature $T_c$ above the boiling point of liquid nitrogen in pressurized La$_3$Ni$_2$O$_{7}$ has sparked a surge of exploration of high-$T_c$ superconductors in the Ruddlesden-Popper (RP) phase nickelates. More recently, the RP phase nicklate La$_5$Ni$_3$O$_{11}$, which hosts layered structure with alternating bilayer and single-layer NiO$_2$ planes, is reported to accommodate SC under pressure, exhibiting a dome-shaped pressure dependence with highest $T_c\approx 64$ K, capturing a lot of interests. Here, using density functional theory (DFT) and random phase approximation (RPA) calculations, we systematically study the electronic properties and superconducting mechanism of this material. Our DFT calculations yield a band structure including two nearly decoupled sets of sub-band structures, with one set originating from the bilayer subsystem and the other from the single-layer one. RPA-based analysis demonstrates that SC in this material occurs primarily within the bilayer subsystem exhibiting an $s^\pm$ wave pairing symmetry similar to that observed in pressurized La$_3$Ni$_2$O$_{7}$, while the single-layer subsystem mainly serves as a bridge facilitating the inter-bilayer phase coherence through the interlayer Josephson coupling (IJC). Since the IJC thus attained is extremely weak, it experiences a prominent enhancement under pressure, leading to the increase of the bulk $T_c$ with pressure initially. When the pressure is high enough, the $T_c$ gradually decreases due to the reduced density of states on the $γ$-pocket. In this way, the dome-shaped pressure dependence of $T_c$ observed experimentally is naturally understood.

Figures (7)

• Figure 1: (color online) Side view of crystal structures of the single-layer (La$_2$NiO$_{4}$), bilayer (La$_3$Ni$_2$O$_{7}$) and SL-BL (La$_5$Ni$_3$O$_{11}$) RP phase nickelates. The blue, grey, and red balls represent lanthanum, nickel, and oxygen atoms, respectively.
• Figure 2: (color online) Band structure of the DFT and six-orbital TB model for La$_5$Ni$_3$O$_{11}$ at 12 GPa. (a) DFT band structure and projected DOS of La$_5$Ni$_3$O$_{11}$. (b) FS in the BZ, with the five pockets labeled. The color scheme in the left half of (b) represents the relative contributions of the $d_{z^2}$ and $d_{x^2-y^2}$ orbital, while the colors scheme on the right half of (b) indicates the relative contributions from Ni atoms in the single-layer and bilayer subsystems. (c) Schematic of La$_5$Ni$_3$O$_{11}$ lattice of six-orbital TB model. The dashed line denotes the $(\frac{1}{2},\frac{1}{2})$ translation of RP stacking between bilayer and single-layer sublattice. (d) The TB band structure corresponding to (c).
• Figure 3: (color online) TB bands and FS characteristics of the BL and SL subsystems in La$_5$Ni$_3$O$_{11}$ (SL-BL system) at 12 GPa. (a) Band structure of the SL-BL system (black lines) and that of the isolated BL subsystem (red lines). (b) FS of the isolated BL subsystem, showing that the $\alpha$ pocket is primarily composed of $d_{x^2-y^2}$ orbitals, the $\beta$ pocket contains contributions from both $d_{x^2-y^2}$ and $d_{z^2}$ orbitals, and the $\gamma$ pocket originates mainly from $d_{z^2}$ orbitals. (c) Band structure of the SL-BL system (black lines) and the isolated SL subsystem (red lines). (d) FS of the isolated SL subsystem, showing that the $\alpha'$ pocket is primarily composed of $d_{x^2-y^2}$ orbitals, the $\gamma'$ pocket originates mainly from $d_{z^2}$ orbitals.
• Figure 4: (color online) (a) Distribution of the largest eigenvalue of the spin susceptibility matrix $\chi^{s}(q)$ in the BZ in the bilayer subsystem for $U = 1$ eV and $J_H = U/6$. The susceptibility peaks at two inequivalent momenta, denoted as Q$_1$ and Q$_2$, respectively. (b) FS of the bilayer subsystem in the BZ at 12 GPa. As shown in (b), Q$_1$ corresponds to a nesting vector between the $\beta$ and $\gamma$ pockets, while Q$_2$ corresponds to a nesting vector between the $\alpha$ and $\beta$ pockets. (c) The largest pairing eigenvalue $\lambda$ of the various pairing symmetries as function of the interaction strength $U$ with fixed $J_H= U/6$. (d) The distributions of the leading $s$-wave pairing gap function on the FS for $U=1.1$ eV, exhibiting an $s^{\pm}$-pattern.
• Figure 5: (color online) Pressure-dependence of the pairing eigen value $\lambda$ (black solid line) and the DOS on the $\gamma$-pocket (red solid line).