Abstract Body

Since the discovery of superconductivity at 80 K in single crystals of La3Ni2O7 at pressures above 14.0 GPa [1-5], extensive efforts have been made to understand the properties of the bilayer nickelate system at both ambient and high pressures. CDW, SDW, structural transition, strange metal behavior, orbital dependent correlations, etc., which are profound in copper oxide and iron-based superconductors, are also present in the pressure-dependent phase diagram of La3Ni2O7. They may be related or irrelevant to the superconductivity of nickelates under pressure. Currently, many questions are open. In this talk, I will briefly introduce the discovery of the superconductivity in La3Ni2O7 and discuss the research progress in nickelate superconductors.

Abstract Body

The recently discovered Ruddlesden-Popper bilayer superconductor La₃Ni₂O₇ has attracted widespread attention due to its superconducting transition temperature exceeding the boiling point of liquid nitrogen, reaching approximately 80 K under a pressure. The superconducting phase under high pressure has an orthorhombic structure of Fmmm space group with the 3d_x2−y2 and 3d_z2 orbitals of Ni cations strongly mixing with oxygen 2p orbitals. Our density functional theory calculations indicate that the superconductivity emerges coincidently with the metallization of the σ-bonding bands under the Fermi level, consisting of the 3d_z2 orbitals with the apical oxygen ions connecting the Ni–O bilayers. Here we propose a bilayer two-orbital model for La₃Ni₂O₇ under high pressure, primarily based on the 3d_x2−y2 and 3d_z2 orbitals of Ni. Through Wannier downfolding and symmetry analysis, we obtain parameters such as electron hopping and site-energy, which provide an excellent description of the electronic band structure and Fermi surface. We find that the Fermi surface of the high-pressure phase consists of three pockets, with α and β being electron pockets, and γ being a hole pocket (mainly originating from the 3d_z2 orbital). To explicitly consider the physics of O-p orbitals, we introduce a higher energy model (eleven-orbital model).  Based on these models, we study the charge transfer, Zhang-Rice singlet bands, pairing symmetry, and superconducting transition temperature in La₃Ni₂O₇. We obtain a comprehensive superconducting phase diagram in the doping plane and find that the La₃Ni₂O₇ under pressure is situated roughly in the optimal doping regime of the phase diagram. Recently, the discovery of superconductivity in Ruddlesden-Popper (RP) La₄Ni₃O₁₀ under pressure has further expanded the realm of nickelate-based superconductor family. Based on the DFT results, we further propose a trilayer two-orbital model by performing Wannier downfolding on Ni-eg orbitals. Our model reveals four Fermi surface sheets with α, β, β′, γ pockets, bearing resemblance to that of bilayer La₃Ni₂O₇. According to the model, our calculated spin susceptibility under random phase approximation predicts an analogous magnetic signal at q = (π/2, π/2), which is more associated with nesting within β, β′ pocktes. Finally, a high energy sixteen-orbital model with direct dp, pp hoppings is proposed, which implies that La₄Ni₃O₁₀ also lies in charge-transfer picture within Zaanen-Sawatzky-Allen scheme. Our exposition of electronic reconstructions and multi-orbital models shed light on theoretical electronic correlation study and experimental exploration for lower pressure in RP series.

References

[1] Nature 621, 493 (2023).

[2] Phys. Rev. Lett. 131, 126001 (2023).

[3]Nature Communications 15，4373 (2024).

[4] SCPMA 67, 117403 (2024).

[5] SCPMA 67, 117402 (2024).

[6] arXiv:2308.16564 (NPJ Quantum Materials accepted).

[7] Phys. Rev. B 110, 014503 (2024).

[8] Chinese Phys. Lett. 41 077402 (2024).

[9] arXiv: 2404.11001

[10] arXiv:2405.19161.

[11] arXiv:2407.19213.

Acknowledgment

This project is supported by NKRDPC-2022YFA1402802, NSFC-92165204, Leading Talent Program of Guangdong Special Projects (201626003), Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices (No. 2022B1212010008), and Guangdong Research Center for Magnetoelectric Physics.

Figure 1. Hopping integrals in the bilayer two-orbital model of La₃Ni₂O₇ with the Ni-𝑑_{𝑥2−𝑦2} (red) and 𝑑_{3𝑧2−𝑟2} (blue) orbitals. (b) Fermi surfaces determined by the bilayer two-orbital model. Reprinted from Ref. [2].

Keywords: High-Tc superconductivity, Nickelate superconductor, Theoretical Models, Pairing symmetry, Pressure

Abstract Body

Superconductors in which the Cooper pairs are mediated by other than phonons attract great theoretical interests since the high-Tc cuprates superconductor was discovered. Many theoretical studies of cuprates have proposed that the pairing may be enhanced by the purely electronic mechanism and the symmetry of superconducting gap functions is d-wave. One of the most standard models is the single orbital Hubbard model on the nearly half-filled square lattice. Since this model is assessed as almost ideal for pairing in several theoretical/numerical assessments, there may be few hope to achieve the improvement of Tc in materials having cuprate-like pairing mechanisms.

Another possible theoretical model of high Tc is the bilayer Hubbard model [1,2]. The two key conclusions of these studies are that so-called s±-wave superconductivity, in which the sign of gap function is the opposite between hole and electron like bands, is realized and Tc is maximized in the nearly half-filled condition. This situation is classified as a spin-fluctuation mediated superconductivity, in which the paring is enhanced by vertical interlayer electron hopping (t_⊥) having several times larger value than that of in-plane hoppings. This condition of t_⊥ cannot be realized in bilayer cuprates because the main bands forming the Fermi surfaces consists of the d_x2-y2 orbitals elongated along in plane directions.

Recently, H. Sun et al. have reported that a Rudlessden-Popper type nickelate La₃Ni₂O₇ exhibits superconductivity about 80 K after structural transition triggered by hydrostatic pressure from Aman to I 4/mmm space group symmetry [3]. In La₃Ni₂O₇, the main bands are formed by the d_x2-y2 and the d_3z2-r2 orbitals, where the vertical hopping t_⊥ of the d_3z2-r2 orbitals is about 5-6 times larger than in-plane one because of orbital elongation along c-axis. Nakata et al. suggested the manifestation of the bilayer model in the I 4/mmm phase and the possibility of superconductivity [4]. However, Ref. [4] only showed the band structure around Fermi level and qualitative discussions, thus multi-band effects and orbital hybridization effects between the d_x2-y2 and the d_3z2-r2 orbitals were unclear.

In order to give more insights, we have studied La₃Ni₂O₇ through deriving and solving a realistic low-energy model by employing first-principles calculation and maximally localized Wannier functions method [5]. The model consists of the d_x2-y2 and d_3z2-r2 orbitals for each two layers. By solving Dyson’s equation based on this model in fluctuation exchange approximation (FLEX), we have obtained the gap functions having the opposite sign bonding- and antibonding- band mainly formed by the d_3z2-r2 orbitals’ coupling (Fig. 2 (d) in Ref. [6]). This can be interpreted as an s±-wave superconductivity assumed in Refs. [1-2, 4]. Through other analyses in Ref. [6], it is found that Tc is expected to be enhanced when the d_3z2-r2 orbitals is nearly half-filled.

To seek further candidates of new superconductors possessing interlayer pairing mechanisms, we have investigated La₄Ni₃O₁₀, a tri-layer counterpart of La₃Ni₂O₇, in a collaboration with Prof. Takano’s experimental Group from NIMS. Firstly, we theoretically calculated a stable crystal structure of La₄Ni₃O₁₀ under pressure and predicted the structural transition above 10 GPa employing first-principles calculations. Subsequently, we applied the same theoretical technique (namely, FLEX) to La₄Ni₃O₁₀ to obtain gap functions. We theoretically concluded that La₄Ni₃O₁₀ may become a superconductor with interlayer pairing mechanism. Finally, the experimental group confirmed superconducting transition at 23 K under pressure of P = 79.2 GPa [7].

In the presentation, we will show the details of these studies and discuss a possible strategy to obtain the new superconductor under ambient pressure.

References

[1] K. Kuroki, T. Kimura, and R. Arita, Phys. Rev. B 66, 184508 (2002).

[2] T. A. Maier and D. J. Scalapino, Phys. Rev. B 84, 180513 (R) (2011).

[3] H. Sun et al., Nature 621, 493 (2023).

[4] M. Nakata, D. Ogura, H. Usui, and K. Kuroki, Phys. Rev. B 95, 214509 (2017).

[5] N. Marzari and D. Vanderbilt, Phys. Rev. B 56, 12847 (1997).

[6] H. Sakakibara, N. Kitamine, M. Ochi, and K. Kuroki, Phys. Rev. Lett. 132, 106002 (2024).

[7] H. Sakakibara et al., Phys. Rev. B 109, 144511 (2024).

Acknowledgment

All contents of this presentation are based on the collaborations with Prof. Kazuhiko Kuroki and Dr. Masayuki Ochi. The author also acknowledges Prof. Yoshihiko Takano, Dr. Hiroya Sakurai, Mr. Hibiki Nagata, Mr. Yuya Ueki, Dr. Kensei Terashima, and Dr. Ryo Matsumoto for collaborations/discussions about La₄Ni₃O₁₀. This presentation is supported by JSPS KAKENHI(Grant No. JP22K03512, JP24K01333) and Advanced Mechanical and Electronic System Research Center in Tottori University. The computing resource is supported by the supercomputer system (system-B) in the Institute for Solid State Physics, the University of Tokyo, and the supercomputer of Academic Center for Computing and Media Studies (ACCMS), Kyoto University.

Abstract Body

Layered perovskite nickelate superconductor La3Ni2O7 (Tc~80K) under high pressure attract much attention due to similarity of crystal structure to high-Tc cuprate. And its superconductivity with high transition temperature (Tc) has been predicted to be unconventional pairing mechanism [1,2]. La₃Ni₂O₇ corresponds to the n = 2 case of the Ruddlesden-Popper phase represented by the general formula of La_n+1Ni_nO3_n+1, and it has two layers of NiO₂ plane. Particularly, La₄Ni₃O₁₀, is corresponding to n = 3 case of the Ruddlesden-Popper phase having triple layers of NiO₂ plane. Due to the similarity between these materials, we expect the possibility of superconductivity in La₄Ni₃O₁₀ under high pressure [3]. We synthesized polycrystalline samples of La₃Ni₂O₇ and La₄Ni₃O₁₀ and measure the temperature dependence of resistance under high pressure. Then we have successfully discovered new superconductor La₄Ni₃O₁₀ under high pressure [4-6].

Transition temperature of high-Tc cuprate is strongly related to carrier density that depends on oxygen content. The same properties are expected also in nickelate superconductors. We have synthesized La₃Ni₂O₇ and La₄Ni₃O₁₀ samples with different oxygen contents and perform resistivity measurements under high pressure. Particularly, La₄Ni₃O₁₀, shows strong oxygen contents dependence of transition temperature, and Tc exceed 36K at 48GPa which is the highest in this system [5]. In my presentation I will talk about detailed superconducting properties.

References

[1] H. Sun et al., Nature 621, 493 (2023).

[2] M. Nakata et al., Phys. Rev. B 95, 214509 (2017).

[3] R. Matsumoto et al., Rev. Sci. Instrum. 87, 076103 (2016).

[4] H. Sakakibara et al., arXiv: 2309.09462. Phys. Rev. B 109, 144511 (2024)

[5] H. Nagata et al., arXiv: 2405.19880.

[6] Y. Ueki et al., arXiv: 2408.04970

Keywords: Superconductivity, Nickelate, High Pressure, Perovskite