AnomalousHc3Hc2nearTcin Pb-In and Critical Phenomena in the Superconducting Sheath

The measured ratio of the critical field for the sheath state to that for the vortex state $\frac{H_{c3\mathrm{}}}{H_{c2\mathrm{}}}$ increases sharply above the Saint James-de Gennes value of 1.695 near $T_c$ in Pb-8.7 at.% In alloy samples with several surface preparations. The sudden increase beginning at temperatures above $0.96T_c$ for the relatively short mean free path Pb-In alloy is in sharp contrast to the precipitous drop of $\frac{H_{c3\mathrm{}}}{H_{c2\mathrm{}}}$ beginning at about 0.85 $T_c$ which has been observed by others in pure Nb and V. The Nb experiment was interpreted in terms of a critical phenomenon. Our observations of anomalous behavior over a narrower reduced temperature interval in the dirty Pb-In alloy than that in clean Nb and V is used (i) to argue that an interpretation of both effects based solely on a critical phenomenon is not valid and (ii) to suggest that neither effect is solely a critical phenomenon. A model recently advanced by Hu which does not appeal to critical phenomena at all may be used to describe both sets of results. In terms of Hu's parameters, the results in Pb-In correspond to $\frac{\delta V}{V_0}\simeq {10}^{-4\mathrm{}}$ and $D>~17\xi \mathrm{}\left(0\right)\mathrm{}$. A simple description of the Pb-In results consistent with Hu's model is that the "critical temperature" of the surface is enhanced by 0.1% relative to that of the bulk.