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arXiv:2606.24126

Fluctuation exchange study on the electron-hole asymmetry of the superconductivity across 1/3 filling in the trilayer Hubbard model

Yushi Yamada, Masataka Kakoi, Masayuki Ochi, Kazuhiko Kuroki

Published Jun 23, 2026• 0 citations
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Abstract

We study within the fluctuation exchange approximation the trilayer Hubbard model where three layers of the Hubbard model are coupled by large interlayer hoppings so that the overlap of the bonding, nonbonding, and antibonding bands is relatively small. We pay special attention to the band fillings close to 1/3, for which the bonding and nonbonding bands as a whole are close to half filling. For relatively small values of the onsite $U$, superconductivity roughly exhibits electron-hole symmetric behavior, as expected for a nearly half-filled two-band system. By contrast, an asymmetry appears when $U$ becomes large, where superconductivity is more favored in the hole-doped regime, i.e., in the regime where electrons are removed from 1/3 filling. We attribute this asymmetry to the asymmetric renormalization of the bonding, nonbonding, and antibonding bands when $U$ is large.

DOI
10.48550/arxiv.2606.24126

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Full or empty narrow bands near the Fermi level are known to enhance superconductivity by promoting scattering processes and spin fluctuations. Here, we demonstrate that doublon-holon fluctuations in systems with half-filled narrow bands can similarly boost the superconducting Tc{T}_{c}Tc​. We study the half-filled attractive bilayer Hubbard model on the square lattice using dynamical mean-field theory. The band structure of the noninteracting system contains a wide band formed by bonding orbitals and a narrow band formed by antibonding orbitals, with bandwidths tunable by the interlayer hopping. The shrinking of the narrow band can lead to a substantial increase in the superconducting order parameter and phase stiffness in the wide band. At the same time, the coupling to the wide band allows the narrow band to remain superconducting---and to reach the largest order parameter---in the flat band limit. We develop an anomalous worm sampling method to study superconductivity in the limit of vanishing effective hopping. By analyzing the histogram of the local eigenstates, we clarify how the interplay between different interaction terms in the bonding/antibonding basis promotes pair fluctuations and superconductivity.
The bilayer Hubbard model with an intra-layer hopping ttt and an inter-layer hopping t⊥t_\perpt⊥​ provides an interesting testing ground for several aspects of what has been called unconventional superconductivity. One can study the type of pair structures which arise when there are multiple Fermi surfaces. One can also examine the pairing for a system in which the structure of the spin-fluctuation spectral weight can be changed. Using a dynamic cluster quantum Monte Carlo approximation, we find that near half-filling, if the splitting between the bonding and anti-bonding bands t⊥/tt_\perp/tt⊥​/t is small, the gap has B1gB_{1g}B1g​ (dx2−y2d_{x^2-y^2}dx2−y2​-wave) symmetry but when the splitting becomes larger, A1gA_{1g}A1g​ (s±s^\pms±-wave) pairing is favored. We also find that in the s±s^\pms± pairing region, the pairing is driven by inter-layer spin fluctuations and that TcT_cTc​ is enhanced.
We study by the Gutzwiller approximation the melting of the valence-bond crystal phase of a bilayer Hubbard model at sufficiently large interlayer hopping. We find that a superconducting domain, with order parameter ${d}_{{z}^{2}\ensuremath{-}{r}^{2}}$, zzz being the interlayer direction and rrr the intralayer one, is stabilized variationally close to the half-filled nonmagnetic Mott insulator. Superconductivity exists at half filling just at the border of the Mott transition and extends away from half filling into a whole region till a critical doping, beyond which it gives way to a normal-metal phase. This result suggests that superconductivity should be unavoidably met by liquefying a valence-bond crystal, at least when each layer is an infinite-coordination lattice and the Gutzwiller approximation becomes exact. Remarkably, this same behavior is well established in the other extreme of two-leg Hubbard ladders, showing it might be of quite general validity.
We propose that when the Fermi level lies within a wide band and also lies close to but not within a coexisting narrow band, high-Tc{T}_{c}Tc​ superconductivity may take place due to the large number of interband pair scattering channels and the small renormalization of the quasiparticles. We show using the fluctuation exchange method that this mechanism works for the Hubbard model on a ladder lattice with diagonal hoppings. From this viewpoint, we give a possible explanation for the low Tc{T}_{c}Tc​ for the actual hole-doped ladder compound, and further predict a higher Tc{T}_{c}Tc​ for the case of electron doping.
The role of near-neighbor electron attraction V V in strongly correlated systems has been at the forefront of recent research of unconventional superconductivity. However, its implications in the doped Hubbard model on expansive systems remain predominantly unexplored. In this study, we employ the density-matrix renormalization group to examine its effect in the lightly doped t t - t' t ′ -Hubbard model on six-leg square cylinders, where t t and t' t ′ are the first and second neighbor electron hopping amplitudes. In the electron-doped regime ( t'>0 t ′ > 0 ), we find that attractive V V can substantially enhance superconducting correlations, driving the system into a pronounced superconducting phase when the attraction exceeds a modest value V_c ≈ 0.5t V c ≈ 0.5 t . In contrast, in the hole-doped regime ( t' <0 t ′ < 0 ), while heightened superconducting correlations have also been observed in the charge stripe phase, the systems remain insulating with pronounced charge density wave order. Our results demonstrate the importance of the electron attraction in boosting superconductivity in broader doped Hubbard systems and highlight the asymmetry between the electron and hole-doped regimes.