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arXiv:1107.0401

Pair Structure and the Pairing Interaction in a Bilayer Hubbard Model

Thomas Maier, Douglas J. Scalapino

Published Jul 2, 2011• 1 citation
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Abstract

The bilayer Hubbard model with an intra-layer hopping $t$ and an inter-layer hopping $t_\perp$ 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 $t_\perp/t$ is small, the gap has $B_{1g}$ ($d_{x^2-y^2}$-wave) symmetry but when the splitting becomes larger, $A_{1g}$ ($s^\pm$-wave) pairing is favored. We also find that in the $s^\pm$ pairing region, the pairing is driven by inter-layer spin fluctuations and that $T_c$ is enhanced.

DOI
10.48550/arxiv.1107.0401

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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.
The bilayer Hubbard model with an intralayer hopping ttt and an interlayer hopping ${t}_{\ensuremath{\perp}}$ 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 antibonding bands ${t}_{\ensuremath{\perp}}/t$ is small, the gap has B1g{B}_{1g}B1g​ (${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave) symmetry, but when the splitting becomes larger, A1g{A}_{1g}A1g​ (${s}^{\ifmmode\pm\else\textpm\fi{}}$-wave) pairing is favored. We also find that in the ${s}^{\ifmmode\pm\else\textpm\fi{}}$ pairing region, the pairing is driven by interlayer spin fluctuations and that Tc{T}_{c}Tc​ is enhanced.
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.
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 ${t}_{\ensuremath{\perp}}$, using many-body perturbation theory and variational methods. They have generally found that superconductivity is enhanced as one of the bands approaches the Lifshitz 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 ${s}^{\ifmmode\pm\else\textpm\fi{}}$ pairing correlations in the large ${t}_{\ensuremath{\perp}}$ 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 Tc{T}_{c}Tc​. 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.
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.
Coupling two strongly correlated layers opens a distinct route to repulsion-driven superconductivity. Yet the same interlayer coupling makes the optimization of superconductivity highly nontrivial. Using the dynamical vertex approximation, we determine the superconducting landscape in the enlarged parameter space spanned by filling and interlayer hopping. We identify an optimal regime at intermediate interlayer hopping and moderate doping away from half filling, where the system exhibits high superconducting transition temperatures (TcT_{\rm c}Tc​) with an interband s±s_{\pm}s±​-wave gap structure. Toward half filling, however, strong self-energy effects can suppress the superconducting tendency by reducing the low-energy spectral weight. We further show that a Fermi-surface distortion induced by longer-range hoppings can weaken this suppression and enhance TcT_{\rm c}Tc​. Our results establish how filling, interlayer hopping, and Fermi-surface geometry jointly optimize the superconducting regime in the strongly correlated bilayer Hubbard model.
We study the Hubbard model on a bilayer with repulsive on-site interactions U in which fermions undergo both intraplane (t) and interplane (tz{\mathit{t}}_{\mathit{z}}tz​) hopping. This situation is what one would expect in high-temperature superconductors such as YBa2{\mathrm{YBa}}_{2}YBa2​Cu3{\mathrm{Cu}}_{3}Cu3​${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathit{y}}$, with two adjacent CuO2{\mathrm{CuO}}_{2}CuO2​ planes. Magnetic and pairing properties of the system are investigated through quantum Monte Carlo simulations for both half- and quarter-filled bands. We find that in all cases interplanar pairing with dx2{\mathit{d}}_{\mathit{x}}^{2}dx2​-z2{\mathit{z}}^{2}z2 symmetry is dominant over planar pairing with dx2{\mathit{d}}_{\mathit{x}}^{2}dx2​-y2{\mathit{y}}^{2}y2 symmetry, and that for a large enough tz{\mathit{t}}_{\mathit{z}}tz​ pair formation is possible through antiferromagnetic correlations. However, another mechanism is needed to make these pairs condense into a superconducting state at lower temperatures. We identify the temperature for pair formation with the spin-gap crossover temperature.