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

We calculate the low-temperature superheating field Bₛₕ of clean superconductors near the boundary between type-I and type-II superconductivity, with particular emphasis on Nb. Ginzburg--Landau theory is not applicable at low temperatures, while previous microscopic calculations have been limited to either the large-$κ$ regime or the dirty limit. The clean, low-$κ$ regime relevant to Nb has therefore remained unresolved. We solve the self-consistent nonlinear nonlocal Eilenberger problem for the Meissner state and then analyze its stability against small perturbations. For a Nb-like material with κGL=0.7, we obtain Bₛₕ 290\, mT at T/Tc=0.2, using Bc0 200\, mT. For a TESLA-shaped Nb accelerator cavity, this corresponds to an intrinsic Meissner-stability limit of about 67\, MV/m.