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arXiv:cond-mat/9502043 · Physical review. B, Condensed matter

Magnetism and pairing in Hubbard bilayers

Raimundo R. dos Santos

Published Jun 1, 1995• 24 citations
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Abstract

We study the Hubbard model on a bilayer with repulsive on-site interactions U in which fermions undergo both intraplane (t) and interplane (${\mathit{t}}_{\mathit{z}}$) hopping. This situation is what one would expect in high-temperature superconductors such as ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathit{y}}$, with two adjacent ${\mathrm{CuO}}_{2}$ 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 ${\mathit{d}}_{\mathit{x}}^{2}$-${\mathit{z}}^{2}$ symmetry is dominant over planar pairing with ${\mathit{d}}_{\mathit{x}}^{2}$-${\mathit{y}}^{2}$ symmetry, and that for a large enough ${\mathit{t}}_{\mathit{z}}$ 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.

DOI
10.1103/physrevb.51.15540

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To understand correlated insulating and unconventional superconducting states in twisted bilayer graphene, we perform a systematic study of spin and pairing correlations in an effective two-orbital Hubbard model, by using the ground-state constrained-path quantum Monte Carlo method. Our numerical simulations reveal that when only the on-site Hubbard UUU is considered, the long-range magnetic order develops for $U\ensuremath{\ge}3.2t$ at half filling. Upon doping away from half filling, an analysis based on the pairing correlations and corresponding vertex contributions identifies that pairing with the d+idd+idd+id symmetry is the dominant pairing channel. As the on-site Coulomb interaction is increased, both spin correlation and effective pairing interaction are enhanced simultaneously, indicating the intimate relation between magnetism and superconductivity. An inclusion of nearest neighbor Coulomb interaction VVV results in a suppression of the d+idd+idd+id superconductivity, but it can survive in the small VVV regime. Our findings are useful for clarifying the ongoing controversy on the superconducting pairing symmetry in twisted bilayer graphene.
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The bilayer Hubbard model describes the antiferromagnet to spin singlet transition and, potentially, aspects of the physics of unconventional superconductors. Despite these important applications, significant aspects of its phase diagram in the interplane hopping ${t}_{\ensuremath{\perp}}$ versus on-site interaction UUU parameter space, at half filling, are largely in disagreement. Here we provide an analysis making use of the average sign of weights over the course of the importance sampling in quantum Monte Carlo simulations to resolve several central open questions. Specifically, this metric of the weights clarifies the finite-sized metallic regimes at small UUU. Furthermore, at strong interactions, it points to the existence of a crossover from a correlated to uncorrelated band insulator not yet explored in a variety of existing, unbiased numerical methods. Our paper demonstrates the versatility of using properties of the weights in quantum Monte Carlo simulations to reveal important physical characteristics of the models under study.
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