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arXiv:2603.25648

Prediction of new superconducting bilayers heterostructures using quantum confinement and proximity effects

Giovanni A. Ummarino, Alessio Zaccone

cond-mat.supr-concond-mat.mes-hallcond-mat.mtrl-sciquant-phSubmitted Mar 26, 2026• Announced Mar 27, 2026
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Abstract

A central challenge in nanoscale superconductivity is to understand and exploit the combined action of quantum confinement and proximity effects in experimentally realistic metallic heterostructures. We theoretically investigate superconducting bilayer heterostructures in which these two effects coexist. Using a generalized Eliashberg framework that incorporates both quantum confinement and proximity coupling, we show that their interplay can substantially enhance the superconducting critical temperature. In particular, the theory predicts superconductivity in selected bilayers whose constituent materials are nonsuperconducting or only weakly superconducting in the bulk. These results identify quantum-confined bilayers as a promising route to engineering emergent superconductivity in metallic heterostructures.

Related papers

Turning non-superconducting elements into superconductors by quantum confinement and proximity

Giovanni A. Ummarino, Alessio Zaccone

Elemental good metals, including noble metals (Cu, Ag, Au) and several $s$-block elements, do not exhibit superconductivity in bulk at ambient pressure, mainly due to weak electron-phonon coupling that cannot overcome Coulomb repulsion. Quantum confinement in ultra-thin films reshapes the electronic spectrum and the density of states near the Fermi level, producing strong, often non-monotonic, thickness dependencies of the critical temperature in established superconductors. Here, we examine whether confinement alone, or combined with proximity effects, can induce superconductivity in metals that are non-superconducting in bulk form. We review recent theoretical progress and introduce a unified framework based on a confinement-generalized, isotropic one-band Eliashberg theory, where the normal density of states becomes energy dependent and key parameters ($E_F$, $λ$, $μ^$) acquire explicit thickness dependence. By numerically solving the Eliashberg equations using ab initio or experimentally determined electron-phonon spectral functions $α^2F(Ω)$ and Coulomb pseudopotentials $μ^$, and without adjustable parameters, we compute the critical temperature $T_c$ as a function of film thickness for representative noble, alkali, and alkaline-earth metals. The results predict that superconductivity emerges only in selected cases and within extremely narrow thickness windows, typically at sub-nanometer scales ($L \sim 0.4-0.6$ nm), indicating strong fine-tuning requirements for confinement-induced superconductivity in good metals. We also consider layered superconductor/normal-metal systems where confinement and proximity effects coexist. In these heterostructures, a substantial enhancement of the critical temperature is predicted, even when the constituent materials are non-superconducting or weak superconductors in bulk form.

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A central challenge in nanoscale superconductivity is to understand and exploit the combined action of quantum confinement and proximity effects in experimentally realistic metallic heterostructures. We theoretically investigate superconducting bilayer heterostructures in which these two effects coexist. Using a generalized Eliashberg framework that incorporates both quantum confinement and proximity coupling, we show that their interplay can substantially enhance the superconducting critical temperature. In particular, the theory predicts superconductivity in selected bilayers whose constituent materials are nonsuperconducting or only weakly superconducting in the bulk. These results identify quantum-confined bilayers as a promising route to engineering emergent superconductivity in metallic heterostructures.
Elemental good metals, including noble metals (Cu, Ag, Au) and several sss-block elements, do not exhibit superconductivity in bulk at ambient pressure, mainly due to weak electron-phonon coupling that cannot overcome Coulomb repulsion. Quantum confinement in ultra-thin films reshapes the electronic spectrum and the density of states near the Fermi level, producing strong, often non-monotonic, thickness dependencies of the critical temperature in established superconductors. Here, we examine whether confinement alone, or combined with proximity effects, can induce superconductivity in metals that are non-superconducting in bulk form. We review recent theoretical progress and introduce a unified framework based on a confinement-generalized, isotropic one-band Eliashberg theory, where the normal density of states becomes energy dependent and key parameters (EFE_FEF​, λλλ, $μ^$) acquire explicit thickness dependence. By numerically solving the Eliashberg equations using ab initio or experimentally determined electron-phonon spectral functions α2F(Ω)α^2F(Ω)α2F(Ω) and Coulomb pseudopotentials $μ^$, and without adjustable parameters, we compute the critical temperature TcT_cTc​ as a function of film thickness for representative noble, alkali, and alkaline-earth metals. The results predict that superconductivity emerges only in selected cases and within extremely narrow thickness windows, typically at sub-nanometer scales (L∼0.4−0.6L \sim 0.4-0.6L∼0.4−0.6 nm), indicating strong fine-tuning requirements for confinement-induced superconductivity in good metals. We also consider layered superconductor/normal-metal systems where confinement and proximity effects coexist. In these heterostructures, a substantial enhancement of the critical temperature is predicted, even when the constituent materials are non-superconducting or weak superconductors in bulk form.
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)].
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.
Superconducting quantum interference devices (SQUIDs) incorporating thin film nanobridges as weak links have sensitivities approaching that required for single spin detection at 4.2 K. However, due to thermal hysteresis they are difficult to operate at much lower temperatures which hinder their application to many quantum measurements. To overcome this, we have developed nanoscale SQUIDs made from titanium-gold proximity bilayers. We show that their electrical properties are consistent with a theoretical model developed for heat flow in bilayers and demonstrate that they enable magnetic measurements to be made on a sample at system temperatures down to 60 mK.
Quantum criticality plays a central role in understanding non-Fermi liquid behavior and unconventional superconductivity in strongly correlated systems. In this review, we explore the quantum critical Eliashberg theory, which extends conventional Eliashberg approaches to non-Fermi liquid regimes governed by critical fluctuations. We discuss the theoretical foundations and recent developments in the field, focusing on the interplay between electronic interactions and bosonic modes near quantum phase transitions as described in the Yukawa-coupled version of the Sachdev–Ye–Kitaev model. Special emphasis is placed on the breakdown of quasiparticle coherence, anomalous scaling behavior, Cooper pairing without quasiparticles, and emergent universality in different physical settings. Starting from a zero-dimensional quantum dot model, we discuss the generalization to higher spatial dimensions and demonstrate the connection between quantum critical Eliashberg theory and holographic superconductivity. Our analysis provides a perspective on how quantum criticality shapes the dynamics of strongly correlated metals and superconductors.
While superconductors are conventionally established by attractive interactions, higher-temperature mechanisms for emergent electronic pairing from strong repulsive electron-electron interactions remain under considerable scrutiny. Here, we establish a strong-coupling mechanism for intertwined superconductivity and magnetic order from purely repulsive interactions in a Kondo-like bilayer system, composed of a two-dimensional Mott insulator coupled to a layer of weakly-interacting itinerant electrons. Combining large scale DMRG and Monte Carlo simulations, we find that superconductivity persists and coexists with magnetism over a wide range of interlayer couplings. We classify the resulting rich phase diagram and find 2-rung antiferromagnetic and 4-rung antiferromagnetic order in one-dimensional systems along with a phase separation regime, while finding that superconductivity coexists with either antiferromagnetic or ferromagnetic order in two dimensions. Remarkably, the model permits a rigorous strong-coupling analysis via localized spins coupled to charge-2e bosons through Kugel-Khomskii interactions, capturing the pairing mechanism in the presence of magnetism due to emergent attractive interactions. Our numerical analysis reveals that pairing remains robust well beyond the strong-coupling regime, establishing a new mechanism for superconductivity in coupled weakly- and strongly-interacting electron systems, relevant for infinite-layer nickelates and superconductivity in moire multilayer heterostructures.