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

TL;DR

This paper reviews and clarifies the applicability of Tc formulas for proximity-coupled thin SN and SS bilayers, emphasizing correct usage in experimental and practical contexts.

Contribution

It clarifies the valid ranges of well-known Tc formulas for SN and SS bilayers, guiding proper application in experiments.

Findings

McMillan's formula is broadly applicable for SN bilayers.

The SS formula has similar reliability to McMillan's.

Guidance is provided for correct formula application in practice.

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.