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.