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arXiv:2203.05669 · Physical review. B./Physical review. B

Enhancing Tc in a composite superconductor/metal bilayer system: A dynamical cluster approximation study

Philip M. Dee, Steven Johnston, Thomas Maier

Published Jun 3, 2022• 11 citations
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Abstract

It has been proposed that the superconducting transition temperature ${T}_{\text{c}}$ of an unconventional superconductor with a large pairing scale but strong phase fluctuations can be enhanced by coupling it to a metal. However, the general efficacy of this approach across different parameter regimes remains an open question. Using the dynamical cluster approximation, we study this question in a system composed of an attractive Hubbard layer in the intermediate coupling regime, where the magnitude of the attractive Coulomb interaction $|U|$ is slightly larger than the bandwidth $W$, hybridized with a noninteracting metallic layer. We find that while the superconducting transition becomes more mean-field-like with increasing interlayer hopping, the superconducting transition temperature ${T}_{\text{c}}$ exhibits a nonmonotonic dependence on the strength of the hybridization ${t}_{\ensuremath{\perp}}$. This behavior arises from a reduction of the effective pairing interaction in the correlated layer that outcompetes the growth in the intrinsic pair-field susceptibility induced by the coupling to the metallic layer. We find that the largest ${T}_{\text{c}}$ inferred here for the composite system is comparable to the maximum value currently estimated for the isolated negative-$U$ Hubbard model.

DOI
10.1103/physrevb.105.214502

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It has been proposed that the superconducting transition temperature Tc{T}_{\text{c}}Tc​ of an unconventional superconductor with a large pairing scale but strong phase fluctuations can be enhanced by coupling it to a metal. However, the general efficacy of this approach across different parameter regimes remains an open question. Using the dynamical cluster approximation, we study this question in a system composed of an attractive Hubbard layer in the intermediate coupling regime, where the magnitude of the attractive Coulomb interaction ∣U∣|U|∣U∣ is slightly larger than the bandwidth WWW, hybridized with a noninteracting metallic layer. We find that while the superconducting transition becomes more mean-field-like with increasing interlayer hopping, the superconducting transition temperature Tc{T}_{\text{c}}Tc​ exhibits a nonmonotonic dependence on the strength of the hybridization t\ensuremath⊥{t}_{\ensuremath{\perp}}t\ensuremath⊥​. This behavior arises from a reduction of the effective pairing interaction in the correlated layer that outcompetes the growth in the intrinsic pair-field susceptibility induced by the coupling to the metallic layer. We find that the largest Tc{T}_{\text{c}}Tc​ inferred here for the composite system is comparable to the maximum value currently estimated for the isolated negative-UUU Hubbard model.
A promising path to realizing higher superconducting transition temperatures TcT_cTc​ is the strategic engineering of artificial heterostructures. For example, quantum materials could, in principle, be coupled with other materials to produce a more robust superconducting state. In this work, we add numerical support to the hypothesis that a strongly interacting superconductor weakened by phase fluctuations can boost its TcT_cTc​ by hybridizing the system with a metal. Using determinant quantum Monte Carlo (DQMC), we simulate a two-dimensional bilayer composed of an attractive Hubbard model and a metallic layer in two regimes of the interaction strength −∣U∣-|U|−∣U∣. In the strongly interacting regime, we find that increasing the interlayer hybridization t⊥t_\perpt⊥​ results in a nonmonotonic enhancement of TcT_cTc​, with an optimal value comparable to the maximum TcT_cTc​ observed in the single-layer attractive Hubbard model, confirming trends inferred from other approaches. In the intermediate coupling regime, when −∣U∣-|U|−∣U∣ is close to the value associated with the maximum TcT_cTc​ of the single-layer model, increasing t⊥t_\perpt⊥​ tends to decrease TcT_cTc​, implying that the correlated layer was already optimally tuned. Importantly, we demonstrate that the mechanism behind these trends is related to enhancement in the superfluid stiffness, as was initially proposed by Kivelson [Physica B: Condensed Matter 318, 61 (2002)].
We study a model of a composite system constructed from a ``pairing layer'' of disconnected attractive-UUU Hubbard sites that is coupled by single-particle tunneling, ${t}_{\ensuremath{\perp}}$, to a disordered metallic layer. For small interlayer tunneling the system is described by an effective long-range XYXYXY phase model whose critical temperature, Tc{T}_{c}Tc​, is essentially insensitive to the disorder and is exponentially suppressed by quantum fluctuations. Tc{T}_{c}Tc​ reaches a maximum for intermediate values of ${t}_{\ensuremath{\perp}}$, which we calculate using a combination of mean-field, classical, and quantum Monte Carlo methods. The maximal Tc{T}_{c}Tc​ scales as a fraction of the zero-temperature gap of the attractive sites when UUU is smaller than the metallic bandwidth, and is bounded by the maximal Tc{T}_{c}Tc​ of the two-dimensional attractive Hubbard model for large UUU. Our results indicate that a thin, rather than a thick, metallic coating is better suited for the enhancement of Tc{T}_{c}Tc​ at the surface of a phase fluctuating superconductor.
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.
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.
In this letter, we have studied the effects of proximity of a superconductor to a normal metal. The system, represented by a bilayer attractive Hubbard model, is investigated using layer-dynamical mean field theory and iterated perturbation theory for superconductivity as an impurity solver. The bilayer system comprises a superconducting and a normal metallic layer, connected by an inter-planar hopping (t⊥t_\perpt⊥​). It is found that superconductivity is induced in the normal layer for small t⊥t_\perpt⊥​. With increasing inter-layer hopping, the bilayer system undergoes two transitions: a first order transition to a normal metallic phase, and subsequently a continuous crossover to a band insulator.
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.