Flat bands promoted by Hund's rule coupling in the candidate double-layer high-temperature superconductor ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$ under high pressure

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Flat bands promoted by Hund's rule coupling in the candidate double-layer high-temperature superconductor ${La}_{3} {Ni}_{2} O_{7}$ under high pressure

Yingying Cao and Yi-feng Yang

Phys. Rev. B 109, L081105 – Published 8 February 2024

Abstract

Experiments in the high-temperature superconductor ${La}_{3} {Ni}_{2} O_{7}$ have revealed both high $T_{c}$ and strange metal behaviors over a wide pressure range. While first-principles density functional theory has predicted weakly correlated bands that cannot explain these key observations, we report here strongly correlated electronic band structure calculations that reveal the dual nature of Ni- $d$ electrons with almost localized $d_{z^{2}}$ orbitals due to on-site Coulomb repulsion and flat bands of Ni- $d_{x^{2} - y^{2}}$ and Ni- $d_{z^{2}}$ quasiparticles near the Fermi energy. We find that the quasiparticle effective masses are greatly enhanced by Hund's rule coupling and their lifetimes are inversely proportional to temperature, which explains the experimentally observed strange metal behavior in the normal state. Our calculations also reveal strong antiferromagnetic spin correlations of Ni- $d$ electrons, which may provide the pairing force of quasiparticles for high-temperature superconductivity. The presence of flat bands and the interplay of orbital-selective Mott, Hund, and Kondo physics lay the basis for a two-component theory of its pairing mechanism and make ${La}_{3} {Ni}_{2} O_{7}$ a unique platform for exploring rich emergent quantum many-body phenomena in the future.

Received 15 July 2023
Revised 8 January 2024
Accepted 9 January 2024

DOI:https://doi.org/10.1103/PhysRevB.109.L081105

Physics Subject Headings (PhySH)

Electronic structure

DFT+DMFT First-principles calculations

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Yingying Cao^1,2 and Yi-feng Yang ^1,2,3,*

¹Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
²University of Chinese Academy of Sciences, Beijing 100049, China
³Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China

^*yifeng@iphy.ac.cn

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Vol. 109, Iss. 8 — 15 February 2024

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Figure 1
(a) High-pressure crystal structure of the candidate high-temperature superconductor ${La}_{3} {Ni}_{2} O_{7}$ visualized by vesta [30]. (b) Orbital-projected band structures and densities of states for Ni- $d$ , O- $p$ , and La- $d$ calculated by DFT at 29.5 GPa, with optimized structural parameters based on experiment [1]. The paths are shown as green lines in the schematic diagram of the Brillouin zone plotted using xcrysden [31], where the local $z$ axis points along the $c$ direction and the $x$ and $y$ axes along the Ni-O bonds in the $a b$ plane. The red points mark the high-symmetry points in the Brillouin zone.
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Figure 2
(a) Orbital-projected spectral function of Ni- $d$ electrons calculated using DFT+DMFT for $U = 5$ eV and $J = 1$ eV at 80 K. The red color is assigned to $d_{x^{2} - y^{2}}$ , blue to $d_{z^{2}}$ , and green to $t_{2 g}$ . Also shown are the corresponding momentum-integrated densities of states, with the three orbital components of $t_{2 g}$ being separated. The orange box highlights the peak from the flat quasiparticle bands of the almost localized $d_{z^{2}}$ orbitals. The gray arrow highlights the lower Hubbard band of Ni- $d_{z^{2}}$ . The $d_{x^{2} - y^{2}}$ orbital shows similar features in the density of states due to its strong hybridization with the $d_{z^{2}}$ orbital. (b) Imaginary part of the orbital-dependent self-energy for $U = 5$ eV and $J = 1$ eV at 80 K. The solid lines are fittings to the data using the fourth-order polynomial, giving an inverse renormalization factor of 5 for $d_{z^{2}}$ and 3 for $d_{x^{2} - y^{2}}$ at the Fermi energy. (c) Temperature dependence of the inverse static local spin susceptibility $1 / χ_{s}$ . The solid line marks a linear-in-temperature fit according to the Curie-Weiss law.
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Figure 3
(a) Orbital-projected spectral function and corresponding densities of states of Ni- $d$ electrons calculated using DFT+DMFT for $U = 5$ eV and $J = 0$ eV at 80 K, plotted as in Fig. 2 showing reduced band renormalization. (b), (c) Inverse renormalization factor of Ni- $d_{z^{2}}$ and Ni- $d_{x^{2} - y^{2}}$ orbitals extracted from the self-energy at 300 K as functions of the Coulomb repulsion $U$ for $J = 0$ and of Hund's rule coupling $J$ for $U = 5$ eV, respectively. (d), (e) The static local spin susceptibility $χ_{s}$ as functions of $U$ for $J = 0$ and of $J$ for $U = 5$ eV, respectively.
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Figure 4
(a) Typical results for the real and imaginary parts of the orbital-dependent self-energy for $d_{z^{2}}$ (blue) and $d_{x^{2} - y^{2}}$ (red) orbitals in real frequency obtained using the maximum entropy method. (b) Temperature dependence of the imaginary part of the self-energy at zero frequency, $- Im Σ (ω = 0)$ , calculated using DFT+DMFT for $U = 5$ eV and $J = 1$ eV. The solid line is a linear-in-temperature fit, showing strange metal behavior as observed in the resistivity measurement above the superconducting transition temperature.
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Flat bands promoted by Hund's rule coupling in the candidate double-layer high-temperature superconductor ${La}_{3} {Ni}_{2} O_{7}$ under high pressure

Yingying Cao and Yi-feng Yang

Phys. Rev. B 109, L081105 – Published 8 February 2024

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Flat bands promoted by Hund's rule coupling in the candidate double-layer high-temperature superconductor La3Ni2O7 under high pressure

Yingying Cao and Yi-feng Yang

Phys. Rev. B 109, L081105 – Published 8 February 2024

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Flat bands promoted by Hund's rule coupling in the candidate double-layer high-temperature superconductor ${La}_{3} {Ni}_{2} O_{7}$ under high pressure