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arXiv:2607.24549

Self-energy pole optimization of superconductivity in the bilayer Hubbard model

Taka-Shi Fujiwara, 志朗 酒井, Ryotaro Arita

Published Jul 27, 2026• 0 citations
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Abstract

We study the real-frequency structure of the self-energy in the bilayer Hubbard model, using the dynamical cluster approximation. At half filling, the Mott insulator-band insulator (MI-BI) crossover involves a rearrangement of self-energy poles between the bonding and antibonding bands; these poles cross as the interlayer hopping $t_{\perp}$ is varied. Upon doping, this pole structure produces a band-selective pseudogap and enhances $s^{\pm}$-wave superconductivity. The order parameter is maximized near the MI-BI boundary, where low-energy anomalous self-energy poles develop simultaneously in both bands and cooperatively enhance the pairing. We further show that these self-energy poles can be interpreted as emergent fermionic excitations, offering an enhanced-pairing mechanism in common with the single-layer Hubbard model. The controllability of these poles through $t_{\perp}$ makes the bilayer system an unconventional platform for optimizing strongly correlated superconductivity.

DOI
10.48550/arxiv.2607.24549

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We study the real-frequency structure of the self-energy in the bilayer Hubbard model, using the dynamical cluster approximation. At half filling, the Mott insulator-band insulator (MI-BI) crossover involves a rearrangement of self-energy poles between the bonding and antibonding bands; these poles cross as the interlayer hopping t⊥t_{\perp}t⊥​ is varied. Upon doping, this pole structure produces a band-selective pseudogap and enhances s±s^{\pm}s±-wave superconductivity. The order parameter is maximized near the MI-BI boundary, where low-energy anomalous self-energy poles develop simultaneously in both bands and cooperatively enhance the pairing. We further show that these self-energy poles can be interpreted as emergent fermionic excitations, offering an enhanced-pairing mechanism in common with the single-layer Hubbard model. The controllability of these poles through t⊥t_{\perp}t⊥​ makes the bilayer system an unconventional platform for optimizing strongly correlated superconductivity.
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The high-temperature superconductivity in copper oxides emerges when carriers are doped into the parent Mott insulator. This well-established fact has, however, eluded a microscopic explanation. Here we show that the missing link is the self-energy pole in the energy-momentum space. Its continuous evolution with doping directly connects the Mott insulator and high-temperature superconductivity. We show this by numerically studying the extremely small doping region close to the Mott insulating phase in a standard model for cuprates, the two-dimensional Hubbard model. We first identify two relevant self-energy structures in the Mott insulator: the pole generating the Mott gap and a relatively broad peak generating the so-called waterfall structure, which is another consequence of strong correlations present in the Mott insulator. We next reveal that either the Mott-gap pole or the waterfall structure (the feature at the energy closer to the Fermi level) directly transforms itself into another self-energy pole at the same energy and momentum when the system is doped with carriers. The anomalous self-energy yielding the superconductivity is simultaneously born exactly at this energy-momentum point. Thus created self-energy pole, interpreted as arising from a hidden fermionic excitation, continuously evolves upon further doping and considerably enhances the superconductivity. Above the critical temperature, the same self-energy pole generates a pseudogap in the normal state. We thus elucidate a unified Mott-physics mechanism, where the self-energy structure inherent to the Mott insulator directly gives birth to both the high critical superconducting temperature and pseudogap.
Fully occupied or unoccupied bands in a solid are often considered inert and irrelevant to a material's low-energy properties. But the discovery of enhanced superconductivity in heavily electron-doped FeSe-derived superconductors poses questions about the possible role of incipient bands (those laying close to but not crossing the Fermi level) in pairing. To answer this question, researchers have studied pairing correlations in the bilayer Hubbard model, which has an incipient band for large interlayer hopping t⊥t_\perpt⊥​, using many-body perturbation theory and variational methods. They have generally found that superconductivity is enhanced as one of the bands approaches the Liftshiz transition and even when it becomes incipient. Here, we address this question using the nonperturbative quantum Monte Carlo (QMC) dynamical cluster approximation (DCA) to study the bilayer Hubbard model's pairing correlations. We find that the model has robust s±s_\pms±​ pairing correlations in the large t⊥t_\perpt⊥​ limit, which can become stronger as one band is made incipient. While this behavior is linked to changes in the effective interaction, we further find that it is counteracted by a suppression of the intrinsic pair-field susceptibility and does not translate to an increased TcT_cTc​. Our results demonstrate that the highest achievable transition temperatures in the bilayer Hubbard model occur when the system has two bands crossing the Fermi level.