Critical fields of weakly coupled superconductors

The parallel critical field of a stack of superconducting and insulating layers is calculated as a function of the superconducting layer's coherence length $\xi$ and thickness $d$ interlayer coherence length ${\xi }_{\perp }$, and insulating thickness $s$. It is shown that the critical field shows an upturn when the stack crosses over from the strongly coupled or three-dimensional regime (${\xi }_{\perp }>s+d$) to the weakly coupled or two-dimensional regime (${\xi }_{\perp }<s+d$). This upturn is a general property of such stacks, though it is more pronounced when $s>d$.