Influence of a Magnetic Field on Tunneling from a Type-II Alloy Superconductor

Planar tunnel diodes have been utilized to study the influence of longitudinal and transverse magnetic fields ($H_{\mathrm{II}}$ and $H_{\perp }$, respectively) on electronic tunneling phenomena involving type-II superconducting alloys (1.1-4.2°K). Each diode consisted of a very thick Pb-Tl alloy film (2.5-7.5 μ, 4.3-13.5 at.% Tl) separated from a much thinner Al film (as thin as ≈200 Å) by an extremely thin (≈30 Å) natural aluminum oxide layer. Zero-field current-voltage ($I-V$) diode characteristics observed with the Al superconducting have demonstrated the existence of a sharply defined alloy energy gap which is essentially independent of alloy composition. With the Al superconducting, very high diode impedances were observed in longitudinal fields for voltages exceeding half the zero-field Al energy gap, suggesting that very nearly all of the alloy surface retains a nonzero energy gap to at least twice the bulk thermodynamic critical field $H_c$. Furthermore, a form of sharp $I-V$ structure persisted to values of $H_{\mathrm{II}}$ satisfying $H_{c1\mathrm{}}<H_{\mathrm{II}}<2\mathrm{}{H}_c$, where $H_{c1\mathrm{}}$ is the Abrikosov lower critical field. This structure has been interpreted tentatively in terms of a field-induced distribution of alloy energy gaps $2{\epsilon }_i$ satisfying ${\epsilon }_m\le {\epsilon }_i\le {\epsilon }_M$, where ${\epsilon }_m$ is the distribution minimum, probably corresponding to the value at the surface, and ${\epsilon }_M$ is the distribution maximum, which approximately equals the zero-field half energy gap. In transverse fields, evidence of superconductivity in the alloy ceases at $H_{\perp }=H_t$, which correlates well numerically with bulk values of the Abrikosov upper critical field $H_{c2\mathrm{}}$. In longitudinal fields, however, evidence of superconductivity was observed to persist to $H_l$, where $\frac{H_l}{H_t}$ ranges between 1.7 and 1.9 depending on alloy composition. The present results indicate rather directly that in longitudinal fields superconductivity persists beyond $H_{c2\mathrm{}}$ within a few coherence lengths of the surface, and extends over a major fraction of the surface. Furthermore, the numerical value of $\frac{H_l}{H_t}$ is in reasonable accord with the sheath critical field ratio predicted by Saint-James and de Gennes for longitudinal fields. For transverse fields, they predict that the sheath will not appear above $H_{c2\mathrm{}}$, consistent with present observations. Taken as a whole, the present measurements are believed to by typical of bulk specimens for which flux entry is delayed to fields substantially greater than $H_{c1\mathrm{}}$ because of surface smoothness.