General trends of superconducting pairing and magnetic correlations in the Ruddlesden-Popper nickelate 𝑚-layered superconductors La𝑚+1⁢Ni𝑚⁢O3⁢𝑚+1

Abstract

We report a comprehensive theoretical analysis of the Ruddlesden-Popper layered nickelates La𝑚+1⁢Ni𝑚⁢O3⁢𝑚+1 (𝑚=1 to 6) under pressure. These materials have recently received significant attention due to the discovery of superconductivity in some nickelates under pressure. Our results suggest that, while these Ruddlesden-Popper layered nickelates display many similarities, they also show noticeable differences. One of the common features of La𝑚+1⁢Ni𝑚⁢O3⁢𝑚+1 is that the electronic states near the Fermi level are mainly contributed by Ni 3⁢𝑑 orbitals, slightly hybridized with O 2⁢𝑝 orbitals. The Ni 𝑑3⁢𝑧2−𝑟2 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 𝑑3⁢𝑧2−𝑟2 and 𝑑𝑥2−𝑦2 orbitals and in-plane intraorbital hopping between 𝑑𝑥2−𝑦2 orbitals was found to be large in La𝑚+1⁢Ni𝑚⁢O3⁢𝑚+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±-wave state driven by spin fluctuations in the bilayer La3⁢Ni2⁢O7 and trilayer La4⁢Ni3⁢O10, two nearly degenerate 𝑑𝑥2−𝑦2-wave and 𝑠±-wave leading states were obtained in the four-layer stacking La5⁢Ni4⁢O13 and five-layer stacking La6⁢Ni5⁢O16. The leading 𝑠±-wave state was recovered in the six-layer material La7⁢Ni6⁢O19 with slightly higher calculated pairing strength 𝜆 than that of the 𝑑𝑥2−𝑦2-wave state. All this evidence suggests that both 𝑠±-wave and 𝑑𝑥2−𝑦2-wave channels are strongly competing in the high-order niceklates based on our random-phase approximation calculations. In general, at the level of the random-phase approximation treatment, the superconducting transition temperature 𝑇𝑐 decreases in stoichiometric bulk systems from the bilayer La3⁢Ni2⁢O7 to the six-layer La7⁢Ni6⁢O19, 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 𝐪=(0.6⁢𝜋,0.6⁢𝜋) for La5⁢Ni4⁢O13 (𝑚=4) and La7⁢Ni6⁢O19 (𝑚=6) and at 𝐪=(0.7⁢𝜋,0.7⁢𝜋) for La6⁢Ni5⁢O16 (𝑚=5). Along the out-of-plane direction, four layers are coupled as ↓−↑−↑−↓ in La5⁢Ni4⁢O13, five layers are coupled as ↑−↑−↓−↑−↑ in La6⁢Ni5⁢O16, and six layers are coupled as ↑−↓−↓−↑−↑−↓ in La7⁢Ni6⁢O19.