On the Applicability Ranges of Tc Formulas for Proximity-Coupled Thin SN and SS Bilayers

Abstract

This brief note revisits the well-established $T_c$ formulas for proximity-coupled thin superconductor-normal conductor (SN) and superconductor-superconductor (SS) bilayers, highlighting their relationships and clarifying their ranges of applicability. Since these formulas are often misapplied in practical contexts, this note provides guidance for their correct use in experimental and applied settings. For SN bilayers, McMillan's formula is recommended for its broad applicability, with its SS counterpart offering similar reliability.

4 pages, 3 figures; the journal version includes supplementary materials with formula derivations and Mathematica code

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