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New Journal of Physics

Pairing correlations in the two-layer attractive Hubbard model

Aleksander Zujev, Richard T. Scalettar, G. G. Batrouni, Pinaki Sengupta

Published Jan 2, 2014• 13 citations
Publisher

Abstract

Studies of systems with two fermionic bands (or equivalently, layers) with repulsive interaction strength U have a long history, with the periodic Anderson model (PAM) being one of the most frequently considered Hamiltonians. In this paper, we use quantum Monte Carlo to study analogous issues for attractive interactions. As in the PAM, we focus on a case where one band (layer) is uncorrelated ( U = 0), and the effect of hybridization V between the bands (layers) on the pairing correlations. A key difference with the PAM is that there is no sign problem, so that we are better able to explore the physics of doped bilayer attractive systems at low temperatures (except in the case of exponentially small transition temperatures) whereas ground state properties of repulsive models can be determined only at half-filling. For small V , pairing in the U < 0 layer induces pairing in the U = 0 layer. At larger V superfluidity is suppressed at the low but finite T at which the quantum Monte Carlo was performed. The quantum Monte Carlo data are complemented by results obtained with the Bogoliubov–de Gennes approximation.

DOI
10.1088/1367-2630/16/1/013004

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Studies of systems with two fermionic bands (or equivalently, layers) with repulsive interaction strength U have a long history, with the periodic Anderson model (PAM) being one of the most frequently considered Hamiltonians. In this paper, we use quantum Monte Carlo to study analogous issues for attractive interactions. As in the PAM, we focus on a case where one band (layer) is uncorrelated ( U = 0), and the effect of hybridization V between the bands (layers) on the pairing correlations. A key difference with the PAM is that there is no sign problem, so that we are better able to explore the physics of doped bilayer attractive systems at low temperatures (except in the case of exponentially small transition temperatures) whereas ground state properties of repulsive models can be determined only at half-filling. For small V , pairing in the U < 0 layer induces pairing in the U = 0 layer. At larger V superfluidity is suppressed at the low but finite T at which the quantum Monte Carlo was performed. The quantum Monte Carlo data are complemented by results obtained with the Bogoliubov–de Gennes approximation.
Studies of systems with two fermionic bands with repulsive interaction strength U have a long history, with the Periodic Anderson Model (PAM) being one of the most frequently considered Hamiltonians. In this paper, we use Quantum Monte Carlo to study analogous issues for attractive interactions. As in the Periodic Anderson Model, we focus on a case where one band is uncorrelated (U=0), and focus on the effect of hybridization V between the bands on the pairing correlations. A key difference with the PAM is that there is no sign problem, so that we are able to explore the physics of doped multi-band attractive systems at low temperatures whereas ground state properties of repulsive models can be determined only at half-filling. For small V, pairing in the U<0 layer induces pairing in the U=0 layer. At larger V the ground state of the coupled system loses its superconducting character. The Quantum Monte Carlo data are complemented by results obtained with the Bogoliubov-de Gennes approximation.
We perform the finite-temperature determinant quantum Monte Carlo simulation for the attractive Hubbard model on the half-filled bilayer square lattice. Recent progress on optical lattice experiments lead us to investigate various single-particle properties such as momentum distribution and double occupancies which should be easily measured in cold-atom experiments. The pair-pair and the density-density correlations have been studied in detail and, through finite-size scaling, we show that there is no competing charge density wave order in the bilayer band-insulator model and that the superfluid phase is the stable phase for the interaction range ∣U∣/t=5−−10|U|/t=5--10∣U∣/t=5−−10. We show the existence of two energy scales in the system as we increase the attractive interaction, one governing the phase coherence and the other one corresponding to the molecule formation. In the end, we map out the full $T\ensuremath{-}U$ phase diagram and compare the Tc{T}_{c}Tc​ obtained through the mean-field analysis. We observe that the maximum Tc/t(=0.27){T}_{c}/t(=0.27)Tc​/t(=0.27) occurs for ∣U∣/t=6|U|/t=6∣U∣/t=6, which is roughly twice the reported Tc{T}_{c}Tc​ of the single-layer attractive Hubbard model.
Motivated by recent experiments realizing correlated phenomena and superconductivity in two-dimensional (2D) van der Waals devices, we consider the general problem of whether correlation effects may be enhanced by modifying band structure while keeping a fixed weak interaction strength. Using determinantal quantum Monte Carlo, we study the 2D Hubbard model for two different band structures: a regular nearest-neighbor tight-binding model and a partially flat-band structure containing a nondispersing region, with identical total noninteracting bandwidth Wtot{W}_{\mathrm{tot}}Wtot​. For both repulsive and attractive weak interactions ($|U|\ensuremath{\ll}{W}_{\mathrm{tot}}$), correlated phenomena are significantly stronger in the partially flat model. In the repulsive case, even with UUU being an order of magnitude smaller than Wtot{W}_{\mathrm{tot}}Wtot​, we find the presence of a Mott insulating state near half filling of the flat region in momentum space. In the attractive case, where generically the ground state is superconducting, the partially flat model exhibits significantly enhanced superconducting transition temperatures. These results suggest the possibility of engineering correlation effects in materials by tuning the noninteracting electronic dispersion.
In previous studies of the half-filled bilayer attractive Hubbard model [Prasad et al., Phys. Rev. A 89, 043605 (2014); Prasad, Phys. Rev. B 106, 184506 (2022)], it has been shown that the clean system has a band-insulator (BI) to superfluid (SF) quantum phase transition. In this paper, we append the effects of random on-site disorder on the kinetic energy, double occupancy, and the pair-pair correlations in the bilayer model. Using the determinant quantum Monte Carlo simulation, we observe that the on-site random disorder plays a significant role in the localization of on-site pairs, and hence in the reduction of the effective hopping. This results in an increase of the double occupancy, which is an effect that is similar to the attractive interaction. We find no change in the critical value of the interaction at which the model undergoes a transition from the BI to SF regime, even though the pair-pair correlations get suppressed for finite on-site disorder strengths Vd/t=0.1{V}_{d}/t=0.1Vd​/t=0.1--0.8. We also confirm that the weak-disorder suppresses the SF phase largely in the strong-coupling limit. Hence the region of the SF phase reduces in the presence of random on-site disorder. Finally, through finite-size scaling, we have estimated the critical disorder strength ${V}_{d}^{c}/t\ensuremath{\sim}1.44$ at ∣U∣/t=5|U|/t=5∣U∣/t=5.
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.