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We have measured the critical current density, superconducting coherence length, and superconducting transition temperature on single-domain, epitaxially-grown Nb(110)/Au(111)/Nb(110) trilayers, all showing non-monotonic behavior as a function of the thickness of the Au layer. To reveal the underlying physical mechanism, we apply the first-principles-based microscopic theory of inhomogeneous relativistic superconductivity which predicts quantitatively the superconducting properties. As a result of the confinement in the growth direction, quantum-well states appear in the Au layer which yields a complex structure of Andreev states in the superconducting state. It is shown how the quantum-well states modify the quasiparticle spectrum and the Josephson supercurrent. Our study reveals the coexistence of the two superconducting phases in the Au layer, the usual intraband s-wave phase and an additional non-uniform phase stemming from interband pairing (without magnetic field). These results indicate the rich interplay between quantum-size and proximity effects, suggesting the possibility of modifying superconducting transport properties by exploiting thickness-dependent quantum size effect
Yamazaki et al. (2024) studied this question.