Energy Gap Measurements by Tunneling between Superconducting Films. II. Magnetic Field Dependence

Abstract

The magnetic field dependence of the energy gap $2\Delta$ was measured by the electron tunneling technique over the temperature interval $T_c\ge T\ge 0.7$ $T_c$ on eight aluminum films ranging in thickness $d$ from 420 to 9850 Å. Measurements of the reduced energy gap versus the reduced field can be represented as a family of curves with a single parameter $\frac{d}{\lambda }$. For $\frac{d}{\lambda }>1\mathrm{}$ the ${\left[\Delta \right(O, T\left)\right]}^2$ versus ${\left[\frac{H}{H_c}\right]}^2$ curves have an initial small negative curvature and then drop abruptly at $H_c$. For $\frac{d}{\lambda }<1\mathrm{}$ the curvature is always positive, decreasing in magnitude as the field increases. For $\frac{d}{\lambda }\approx 1$ we obtain an almost straight line. The results are qualitatively as predicted by the Ginzburg-Landau (GL) equations for $\frac{d}{\lambda }\ge 1$ but not for $\frac{d}{\lambda }<1\mathrm{}$. It is suggested that this discrepancy with solutions of the GL equations may arise from the breakdown of the assumption that the order parameter is independent of position. Measurements on a lead film of thickness 1000 Å at $\frac{T}{T_c}=0.14\mathrm{}$ showed that the energy gap goes smoothly to zero with positive curvature as $H$ approaches $H_c$.