General trends of electronic structures, superconducting pairing, and magnetic correlations in the Ruddlesden-Popper nickelate $m$-layered superconductors La$_{m+1}$Ni$_{m}$O$_{3m+1}$

TL;DR

This study maps the electronic structure, superconducting tendencies, and magnetic correlations of the Ruddlesden–Popper nickelates La$_{m+1}$Ni$_m$O$_{3m+1}$ for m = 1–6 under pressure using DFT with maximally localized Wannier functions and a multiorbital Hubbard model treated in random-phase approximation. A two-$e_g$-orbital picture emerges with a pressure-tunable bonding–antibonding splitting in the $d_{3z^2-r^2}$ sector and increasing in-plane hybridization as $m$ grows, shaping the Fermi surface and pairing channels. Across the higher-$m$ members, the leading superconducting instabilities transition from robust $s^ ext{±}$ in bilayer/trilayer to near-degenerate $d_{x^2-y^2}$-wave and $s^ ext{±}$-wave in $m=4,5$, and a recovered $s^ ext{±}$-wave dominance in the six-layer case, with a general decrease of $T_c$ predicted in stoichiometric bulk by RPA. Magnetic correlations display in-plane q-vectors around $(0.6 ext{π},0.6 ext{π})$ to $(0.7 ext{π},0.7 ext{π})$ depending on $m$, and interlayer couplings evolve from ferromagnetic to antiferromagnetic as $m$ increases, indicating rich, layer-specific spin dynamics. Overall, the work delineates systematic trends in pairing and magnetism across RP nickelates under pressure and provides a quantitative foundation to guide experimental exploration of higher-order nickelate superconductors.

Abstract

We report a comprehensive theoretical analysis of the Ruddlesden-Popper layered nickelates La$_{m+1}$Ni$_m$O$_{3m+1}$ ($m = 1$ to 6) under pressure. Our results suggest that, while these Ruddlesden-Popper layered nickelates display many similarities, they also show noticeable differences. The Ni $d_{3z^2-r^2}$ orbitals display bonding-antibonding, or bonding-antibonding-nonbonding, characteristic splittings, depending on the even or odd number of stacking layers $m$. In addition, the ratio of the in-plane interorbital hopping between $d_{3z^2-r^2}$ and $d_{x^2-y^2}$ orbitals and in-plane intraorbital hopping between $d_{x^2-y^2}$ orbitals was found to be large in La$_{m+1}$Ni$_m$O$_{3m+1}$ ($m = 1$ to 6), and this ratio increases from $m = 1$ to $m = 6$, suggesting that the in-plane hybridization will increase as the layer number $m$ increases. In contrast to the dominant $s^\pm$--wave state driven by spin fluctuations in the bilayer La$_3$Ni$_2$O$_7$ and trilayer La$_4$Ni$_3$O$_{10}$, two nearly degenerate $d_{x^2-y^2}$-wave and $s^\pm$-wave leading states were obtained in the four-layer stacking La$_5$Ni$_4$O$_{13}$ and five-layer stacking La$_6$Ni$_5$O$_{16}$. The leading $s^\pm$-wave state was recovered in the six-layer material La$_7$Ni$_6$O$_{19}$. In general, at the level of the random phase approximation treatment, the superconducting transition temperature $T_c$ decreases in stoichiometric bulk systems from the bilayer La$_3$Ni$_2$O$_7$ to the six-layer La$_7$Ni$_6$O$_{19}$, despite the $m$ dependent dominant pairing. Both in-plane and out-of-plane magnetic correlations are found to be quite complex. Within the in-plane direction, we obtained the peak of the magnetic susceptibility at ${\bf q} = (0.6 π, 0.6 π)$ for La$_5$Ni$_4$O$_{13}$ and La$_7$Ni$_6$O$_{19}$, and at ${\bf q} = (0.7 π, 0.7 π)$ for La$_6$Ni$_5$O$_{16}$.

Figures (8)

• Figure 1: Schematic crystal structures of the RP perovskite family La$_{m+1}$Ni$_m$O$_{3m+1}$ (green = La; blue = Ni; red = O). The visualization code VESTA is used Momma:vesta.
• Figure 2: (a) Schematic electronic densities of $3d$-electrons per Ni for different $m$-layer stacking RP nickelates La$_{m+1}$Ni$_m$O$_{3m+1}$. (b-e) Sketches of electronic states for two "active" $e_g$ orbitals in La$_{m+1}$Ni$_m$O$_{3m+1}$ with layers (b) $m = 1$, (c) $m = 2, 4, 6$, and (d) $m = 3, 5$ and (e) $\infty$, respectively. The light blue and pink horizontal lines represent $d_{3z^2-r^2}$ and $d_{x^2-y^2}$ states, respectively. The solid circles indicate the occupied electrons of $e_g$ orbitals in the stoichiometric ratio La$_{m+1}$Ni$_{m}$O$_{3m+1}$.
• Figure 3: Band structures of the tight-binding models for La$_{m+1}$Ni$_m$O$_{3m+1}$ ($m$ = 1 to 6) at 30 GPa. The coordinates of the high symmetry points in the Brillouin zone are $\Gamma$ = (0, 0, 0), X = (0, 0.5, 0), and M = (0.5, 0.5, 0). Here, two $e_g$ orbitals were considered in the tight-binding models with an overall filling of $n = 2$ to 7 for $m = 1$ to 6 (e.g., 1.2 electrons per site for $m = 6$).
• Figure 4: Fermi surfaces of the tight-binding models for La$_{m+1}$Ni$_m$O$_{3m+1}$ ($m$ = 1 to 6) at 30 GPa. Here, two $e_g$ orbitals were considered in the tight-binding models with an overall filling of $n = 2$ to 7 for $m = 1$ to 6 (e.g., 1.2 electrons per site for $m = 6$).
• Figure 5: The RPA calculated leading superconducting singlet gap structures $g_\alpha({\bf k})$ for momenta ${\bf k}$ on the Fermi surfaces for (a) La$_5$Ni$_4$O$_{13}$, (b) La$_6$Ni$_5$O$_{16}$, and (c) La$_7$Ni$_6$O$_{19}$ with corresponding pairing strengths $\lambda$ at 30 GPa. The sign of $g_\alpha({\bf k})$ is indicated by the color (red = positive, blue = negative), and its amplitude by the color darkness. We used Coulomb parameters $U=1.4$ eV, $U'=U/2$, and $J=J'=U/4$. The calculation was performed at $T=0.01$ eV.