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

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.

Figures (9)

• Figure 1: Schematic illustration of the confinement-induced reconstruction of the Fermi surface in a metallic thin film. (Left) For weak confinement, the bulk Fermi sphere is partially depleted by two symmetric hole-like regions along the confinement direction, corresponding to suppressed electronic states. (Right) Below a critical thickness, the overlap of these excluded regions leads to a topological transformation of the Fermi surface into a non-simply-connected geometry. The orange bars indicate the film thickness $L$, highlighting the role of spatial confinement in driving the topological crossover.
• Figure 2: Physical parameters used in the theory for films of different materials: Cu ($\lambda$ (black solid line) and $\mu^{*}$ (black dashes line)), Ag ($\lambda$ (red solid line) and $\mu^{*}$ (red dashes line)) and Au ($\lambda$ (green solid line) and $\mu^{*}$ (green dashes line)). All parameters are plotted as a function of the film thickness $L$.
• Figure 3: Critical temperature $T_c$ versus film thickness $L$: full solid line represent the numerical solutions of Eliashberg equations. Cu (black solid line), Ag (red solid line) and Au (green solid line). In the inset, the Eliashberg electron-phonon spectral function of these elements are shown: Cu (black solid line), Ag (red solid line) and Au (green solid line).
• Figure 4: Physical parameters used in the theory for films of different materials: Li ($\lambda$ (black solid line) and $\mu^{*}$ (black dashes line)), Na ($\lambda$ (red solid line) and $\mu^{*}$ (red dashes line)) and K ($\lambda$ (blue solid line) and $\mu^{*}$ (green dashes line)). Rb ($\lambda$ (red solid line) and $\mu^{*}$ (blue dashes line)) and Cs ($\lambda$ (orange solid line) and $\mu^{*}$ (orange dashes line)). All parameters are plotted as a function of the film thickness $L$.
• Figure 5: Critical temperature $T_c$ versus film thickness $L$: full circles represent the numerical solutions of Eliashberg equations for obtaining the maximum $T_c$. Li (black full circle), Na (red full circle), K (green full circle), Rb (blue full circle) and Cs (orange full circle). In the inset, the Eliashberg electron-phonon spectral function of these elements are shown: Li (black solid line), Na (red solid line), K (green solid line), Rb (blue solid line) and Cs (orange solid line).