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arXiv:2602.07585

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

Giovanni A. Ummarino, Alessio Zaccone

cond-mat.supr-concond-mat.mes-hallcond-mat.mtrl-sciphysics.app-phquant-phSubmitted Feb 7, 2026• Announced Feb 10, 2026
v1 · Feb 7, 2026v2 · Feb 11, 2026v3 · Apr 8, 2026
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Abstract

Elemental good metals, including noble metals (Cu, Ag, Au) and several $s$-block elements, do not exhibit superconductivity in bulk at ambient pressure, primarily due to weak electron--phonon coupling that fails to overcome Coulomb repulsion. In this perspective, we examine whether quantum confinement alone, or in combination with proximity effects, can induce an observable superconducting instability in metals that are non-superconducting in bulk form. We review recent theoretical progress and present a unified framework based on a confinement-generalized, isotropic one-band Eliashberg theory, in which the normal density of states becomes energy dependent and key material parameters ($E_F$, $λ$, and $μ^{*}$) acquire an explicit thickness dependence. By numerically solving the resulting Eliashberg equations using ab-initio or experimentally determined electron--phonon spectral functions $α^{2}F(Ω)$ and Coulomb pseudopotentials $μ^{*}$, and without introducing adjustable parameters, we compute the critical temperature $T_c$ as a function of film thickness for representative noble, alkali, and alkaline-earth metals. The theory predicts that superconductivity can emerge only in selected cases and within extremely narrow thickness windows, typically centered around sub-nanometer scales ($L \sim 0.4$--$0.6$~nm). We further discuss layered superconductor/normal-metal systems, where quantum 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 poor superconductors in bulk form.

Journal reference
Journal of Physics: Condensed Matter 38 143003 (2026)
DOI
10.1088/1361-648X/ae5907

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Scientific Reports•Jun 21, 2017•2 citations
Elemental good metals, including noble metals (Cu, Ag, Au) and several sss-block elements, do not exhibit superconductivity in bulk at ambient pressure, primarily due to weak electron--phonon coupling that fails to overcome Coulomb repulsion. In this perspective, we examine whether quantum confinement alone, or in combination with proximity effects, can induce an observable superconducting instability in metals that are non-superconducting in bulk form. We review recent theoretical progress and present a unified framework based on a confinement-generalized, isotropic one-band Eliashberg theory, in which the normal density of states becomes energy dependent and key material parameters (EFE_FEF​, λλλ, and μ∗μ^{*}μ∗) acquire an explicit thickness dependence. By numerically solving the resulting Eliashberg equations using ab-initio or experimentally determined electron--phonon spectral functions α2F(Ω)α^{2}F(Ω)α2F(Ω) and Coulomb pseudopotentials μ∗μ^{*}μ∗, and without introducing adjustable parameters, we compute the critical temperature TcT_cTc​ as a function of film thickness for representative noble, alkali, and alkaline-earth metals. The theory predicts that superconductivity can emerge only in selected cases and within extremely narrow thickness windows, typically centered around sub-nanometer scales (L∼0.4L \sim 0.4L∼0.4--0.60.60.6~nm). We further discuss layered superconductor/normal-metal systems, where quantum 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 poor superconductors in bulk form.
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.
We develop a Ginzburg-Landau theory for superconducting thin films under quantum confinement. Starting from the Ginzburg-Landau theory and the recently developed confinement theory of metallic thin films, explicit analytical expressions are derived for the coherence length, penetration depth, electronic mean free path, and Ginzburg-Landau parameter in confined geometries. The central result is that quantum confinement directly renormalizes the intrinsic superconducting coherence length through confinement-induced modifications of the electronic density of states and Fermi energy. This effect is absent in conventional thin-film transport theories based solely on surface scattering. As a consequence, confinement simultaneously suppresses the coherence length and enhances the penetration depth, thereby driving superconductors toward stronger type-II behavior over a broad thickness range. The interplay between quantum confinement and disorder can also produce reentrant type-I/type-II crossovers. The theory predicts a crossover regime in which confinement-induced renormalization of superconducting length scales and transport scattering become strongly intertwined. Comparison with recent penetration-depth measurements in Al thin films shows that the observed enhancement of the penetration depth originates from the interplay between confinement-induced renormalization of the coherence length and suppression of the effective mean free path by surface and disorder scattering. The results establish a direct connection between quantum confinement and superconducting electrodynamics in confined metallic films.
Quantum confinement restructures the electronic phase space of ultrathin metals, but the resulting density-of-states (DOS) change is not generically large. We show that, within a three-dimensional confinement theory based on the suppression of long-wavelength electronic states, the Fermi-level DOS enhancement on the weak-confinement branch is bounded by (4/3)1/3−1≃10.1%(4/3)^{1/3}-1\simeq10.1\%(4/3)1/3−1≃10.1%. Instead, confinement-induced redistribution of electronic phase space can be strongly amplified by resonant denominators in the second-order susceptibility. A minimal double-resonance closure predicts giant amplification when the film thickness approaches Lc=(2π/n)1/3L_c=(2π/n)^{1/3}Lc​=(2π/n)1/3, where nnn is the carrier density, and a dominant optical pathway lies within a dephasing linewidth of resonance. Applied to recent Ag(111) measurements, the theory gives an effective phase-space carrier density parameter neff≃3.6×1020 cm−3n_{\rm eff}\simeq3.6\times10^{20}\,\mathrm{cm}^{-3}neff​≃3.6×1020cm−3, a tenfold enhancement of ∣χ(2)∣|χ^{(2)}|∣χ(2)∣, and hence the observed ∼100\sim100∼100-fold increase of thickness-normalized second-harmonic-generation efficiency, together with the observed non-oscillatory thickness dependence.
A central unresolved question in the theory of superconductivity is why only a small subset of metallic elements exhibit a superconducting state, whereas many others remain strictly normal. Neither the conventional Bardeen Cooper Schrieffer (BCS) framework nor its extensions involving charge density wave (CDW) or pair density wave (PDW) order provide a predictive or material-selective criterion capable of distinguishing superconducting metals from non-superconducting ones. In particular, the persistent absence of superconductivity in simple noble metals with well-defined Fermi surfaces poses a challenge for all traditional approaches. Here we address this problem using the Modulated Electron Lattice (MEL) Ginzburg Landau (GL) framework introduced in our previous work. In this formulation, a coarse-grained MEL charge field ρMEL(r)ρ_{\mathrm{MEL}}(\mathbf{r})ρMEL​(r) with momentum dependent stiffness α(q)α(q)α(q) is coupled to the superconducting (SC) order parameter ψ(r)ψ(\mathbf{r})ψ(r). We show that metallic superconductivity emerges only when the system satisfies a specific ``MEL enhancement window,'' characterized by a negative minimum of α(q)α(q)α(q) at either a finite modulation wave vector q∗q^{\ast}q∗ or at q=0q=0q=0, together with sufficiently strong coupling between ρMELρ_{\mathrm{MEL}}ρMEL​ and ψψψ. This unified criterion naturally partitions metallic elements into three universal classes: (i) MEL-enhanced superconductors with a finite-q∗q^{\ast}q∗ charge mode, (ii) conventional BCS superconductors as the homogeneous q∗=0q^{\ast}=0q∗=0 limit of the MEL framework, and (iii) metals for which α(q)α(q)α(q) remains positive for all qqq, suppressing all MEL modes and preventing any superconducting instability. By applying this criterion to simple metallic elements, we identify why some metals develop superconductivity while others do not, possibly resolving a selection problem long open within the BCS paradigm.
Ultra-thin films are fundamental components of modern nanoelectronics, where reducing thickness to the few-nanometer scale leads to a dramatic increase in electrical resistivity. For decades, this behavior has been interpreted in terms of classical size effects, primarily surface scattering within the Fuchs--Sondheimer theory and grain-boundary scattering in the Mayadas--Shatzkes model. While these approaches successfully describe transport when the film thickness is comparable to the electronic mean free path, growing experimental evidence indicates that they become insufficient under extreme confinement. This review discusses the crossover from classical scattering to a quantum-confinement regime in which the electronic states available for transport are fundamentally restructured by finite size. We review the recently proposed reciprocal-space confinement theory, which predicts an exponential increase of resistivity with decreasing thickness at the nanoscale, and discuss how it can be combined with classical surface-scattering models to provide a unified description of ultra-thin metallic and semiconducting films. Finally, we summarize recent experimental evidence supporting this picture and discuss its implications for future nanoelectronic devices, nanoscale interconnects, and quantum transport under extreme spatial confinement.
In this research, we tailor the phonon density of states (DOS) in thin superconducting films to suppress quasiparticle losses. We examine a model system of a proximity-enhanced three-layered Al/Nb/Al heterostructure and show that the local quantized phonon spectrum of the ultrathin Al cladding layers in the heterostructure has a pronounced effect on the superconducting resonator's quality factors. Instead of a monotonic increase of quality factors with decreasing temperatures, we observe the quality factor reaches a maximum at 1.2 K in 5/50/5 nm Al/Nb/Al microstrip resonators, because of a quantized phonon ladder. The phonon DOS may be engineered to enhance the performance of quantum devices.