Hund's Rule, Interorbital Hybridization, and High-$T_c$ Superconductivity in the Bilayer Nickelate

Abstract

Understanding the pairing mechanism in bilayer nickelate superconductors constitutes a fascinating quest. Here we investigate the intriguing interplay between Hund's rule coupling and interorbital hybridization in a two-orbital model for bilayer nickelates, using a comprehensive tensor network approach: density matrix renormalization group for finite-size systems, infinite projected entangled-pair states in the thermodynamic limit, and thermal tensor networks for finite-temperature properties. We explain the pressure-dependent high-$T_c$ superconductivity observed in experiment, by identifying three distinct superconductive (SC) regimes: hybridization dominant, Hund's rule dominant, and the hybrid-Hund synergistic SC regimes. In these SC regimes, both $d_{x^2-y^2}$ and $d_{z^2}$ orbitals exhibit algebraic pairing correlations with similar Luttinger parameters $K_{\mathrm{SC}}$. However, the former exhibits a much stronger amplitude than the latter, with a distinctly higher SC characteristic temperature $T_c^{\ast }$, below which the pairing susceptibility diverges as ${\chi }_{\mathrm{SC}}(T)\sim 1/T^{2-K_{\mathrm{SC}}}$. With realistic model parameters, we find the pressurized La${}_3$Ni${}_2$O${}_7$ falls into the Hund's rule dominated SC regime. As hybridization further enhances with pressure, it leads to significant interorbital frustration and in turn suppresses the SC correlations, explaining the rise and fall of high-$T_c$ superconductivity under high pressure. Our results offer a comprehensive understanding of the interlayer pairing in superconducting La${}_3$Ni${}_2$O${}_7$.

5+5 pages, 4+5 figures

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Cited by in corpus (6)

• Strong-coupling study of the pairing mechanism in pressurized La${}_3$Ni${}_2$O${}_7$
• Strain-Engineered Electronic Structure and Superconductivity in La${}_3$Ni${}_2$O${}_7$ Thin Films
• Unifying Strain-driven and Pressure-driven Superconductivity in La${}_3$Ni${}_2$O${}_7$: Suppressed charge/spin density waves and enhanced interlayer coupling
• Charge distribution and magnetism in bilayer La${}_3$Ni${}_2$O${}_7$: a hybrid functional study
• Orbital-selective electron correlations in high-$T_{\mathrm{c}}$ bilayer nickelates: from a global phase diagram to implications for spectroscopy
• Magnetically Mediated Cross-Layer Pairing in Pressurized Trilayer Nickelate La${}_4$Ni${}_3$O${}_{10}$