Electronic structures and superconductivity in Nd-doped La$_3$Ni$_2$O$_7$

TL;DR

The paper addresses how Nd substitution in the bilayer RP nickelate La$_3$Ni$_2$O$_7$ modulates superconductivity. It combines density functional theory (DFT) with renormalized mean-field theory (RMFT) to link chemical pressure effects to orbital-resolved electronic structure, constructing bilayer two-orbital and extended 11-orbital descriptions and deriving interlayer $J_ot^z$ to assess pairing. A robust finding is a persistent $s_ ext{±}$-wave pairing symmetry with a non-monotonic Tc, peaking near ~70% Nd doping due to the competition between enhanced interlayer superexchange and decreasing particle density. The work highlights orbital-selective responses to chemical doping and provides design principles for achieving higher $T_c$ in RP nickelates through targeted orbital control and structural tuning.

Abstract

The recent discovery of high-$T_c$ superconductivity in Ruddlesden-Popper (RP) nickelates has motivated extensive efforts to explore higher $T_c$ superconductors. Here, we systematically investigate Nd-doped La$_3$Ni$_2$O$_7$ using density functional theory (DFT) and renormalized mean-field theory (RMFT). DFT calculations reveal that both the lattice constants and interlayer spacing decrease upon Nd substitution, similar to the effect of physical pressure. However, the in-plane Ni-O-Ni bond angle evolves non-monotonically with doping, increasing to a maximum at 70% (~2/3) Nd doping level and then falling sharply at 80%, which leads to a reduction in orbital overlap. Moreover, Nd doping has a more pronounced effect on the Ni-$d{_{z^2}}$ orbital, demonstrating an orbital-dependent effect of rare-earth substitution. Through the bilayer two-orbital t-J model, RMFT analysis further shows an $s\pm$-wave pairing symmetry, with $T_c$ rising to a maximum at about 70% Nd substitution before declining, in agreement with the transport measurements. The variation in $T_c$ can be traced to the competition between continuously enhanced interlayer superexchange coupling $J_\perp^z$ and a gradual decrease in particle density. These results highlight the delicate interplay among structural tuning, orbital hybridization, and superconductivity, providing important clues to design higher-$T_c$ RP nickelate superconductors.

Figures (5)

• Figure 1: (a) Crystal structure of Nd-doped La$_{3}$Ni$_2$O$_7$. The blue, yellow, red and grey balls denote La, Nd O, and Ni atoms. $d_\perp$ and $r_z$ indicate the interlayer Ni distance and the apical Ni-O bond length respectively. (b) Interlayer distance and apical Ni-O bond length versus doping level. (c) Ni-O-Ni angle versus doping level. (d) Band structures and projected DOS of Nd-doped La$_3$Ni$_2$O$_7$ at varying doping level under high pressure.
• Figure 2: (a) Band structure and (b) FS of bilayer two-orbital model for 70% Nd-doped La$_3$Ni$_2$O$_7$. The color bar indicates the orbital weight of Ni-$d_{z^{2}}$ and $d_{x^{2}-y^{2}}$. The grey lines in (a) are band structures from DFT. (c)-(d) Variation with doping level of (c) interlayer $d_{z^2}$ and $d_{x^2-y^2}$ hoppings, (d) density of $d_{z^2}$ and $d_{x^2-y^2}$ orbitals.
• Figure 3: (a) Band structure and (b) FS of eleven-orbital model for 70% Nd-doped La$_3$Ni$_2$O$_7$. The blue, red, and green colors in (a) denote orbital weight of Ni-$d_{z^{2}}$, Ni-$d_{x^{2}-y^{2}}$ and O-$p$ orbitals. The color bar in (b) indicates the orbital weight of Ni-$d_{3z^{2}-r^{2}}$ and $d_{x^{2}-y^{2}}$. The grey lines in (a) are band structures from DFT.
• Figure 4: Variation with doping level of (a) interlayer $d_{z^2}$ superexchange coupling and (b) transition temperature $T_c$.
• Figure 5: (a) The projection of energy gap on FS and (b) evolution of the energy gap with temperature for different pairing bonds at 70% Nd-doping level. Here $g_t^{z/x}$ denotes the renormalization factor for $d_{z^2}/d_{x^2-y^2}$ orbital, and $\Delta_{\bot/||}^{z/x}$ is the interlayer/in-plane pairing bond for $d_{z^2}/d_{x^2-y^2}$ orbital.