Magnetic Field Dependence of Energy Gap in Superconductors

The dependence of energy gap in superconductors on static magnetic fields has been derived in a gauge-invariant way from the theory of Bardeen, Cooper, and Schrieffer. It has been shown that the gap width decreases with magnetic field approaching the critical value. Optimum conditions have been discussed for the observation of such an effect. The decrease in gap width has been calculated for two supreconductors, Al and Sn, and it has been shown that for film thickness between ${10}^{-4\mathrm{}}$ to ${10}^{-5\mathrm{}}$ cm, the effect can be large enough to be observable.