Superheating field of clean superconductors near the type-I--type-II boundary: the low-temperature Meissner stability limit of niobium

Abstract

We calculate the low-temperature superheating field $B_{\mathrm{sh}}$ of clean superconductors near the boundary between type-I and type-II superconductivity, with particular emphasis on Nb. The calculation is based on the self-consistent nonlinear nonlocal Eilenberger theory and the linear stability analysis of the Meissner state. For a Nb-like material with ${\kappa }_{\mathrm{GL}}=0.7$, we obtain $B_{\mathrm{sh}}\simeq 290\mathrm{mT}$ at $T/T_c=0.2$, using $B_{c0}\simeq 200\mathrm{mT}$. This value is substantially higher than the value obtained by naively extrapolating the Ginzburg--Landau result near $T_c$ to $T\ll T_c$. For a TESLA-shaped Nb accelerator cavity, it corresponds to an intrinsic Meissner-stability limit of about $67MV/m$.

4 pages, 1 figure