Energy Gap Measurements by Tunneling between Superconducting Films. II. Magnetic Field Dependence
Abstract
The magnetic field dependence of the energy gap $2\ensuremath{\Delta}$ was measured by the electron tunneling technique over the temperature interval ${T}_{c}\ensuremath{\ge}T\ensuremath{\ge}0.7$ ${T}_{c}$ on eight aluminum films ranging in thickness $d$ from 420 to 9850 \AA{}. Measurements of the reduced energy gap versus the reduced field can be represented as a family of curves with a single parameter $\frac{d}{\ensuremath{\lambda}}$. For $\frac{d}{\ensuremath{\lambda}}>1$ the ${[\ensuremath{\Delta}(O, T)]}^{2}$ versus ${[\frac{H}{{H}_{c}}]}^{2}$ curves have an initial small negative curvature and then drop abruptly at ${H}_{c}$. For $\frac{d}{\ensuremath{\lambda}}<1$ the curvature is always positive, decreasing in magnitude as the field increases. For $\frac{d}{\ensuremath{\lambda}}\ensuremath{\approx}1$ we obtain an almost straight line. The results are qualitatively as predicted by the Ginzburg-Landau (GL) equations for $\frac{d}{\ensuremath{\lambda}}\ensuremath{\ge}1$ but not for $\frac{d}{\ensuremath{\lambda}}<1$. 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 \AA{} at $\frac{T}{{T}_{c}}=0.14$ showed that the energy gap goes smoothly to zero with positive curvature as $H$ approaches ${H}_{c}$.