Dependence of the Energy Gap in Superconductors on Position and Magnetic Field

A review is given of work concerning the decrease of the energy gap in superconductors when a magnetic field is applied. The absence of any observable effect in previous spectroscopic work is explained, and conditions for large effects are outlined. Experimental measurements on thermal conductivity and microwave absorption in films in a magnetic field are described. The results show that in thin films, the gap can be depressed continuously to zero, yielding a second-order phase transition. In thicker films, the gap can be only partially depressed before the transition, and the transition is of first order. These results agree with those obtained theoretically by Douglass from the Ginzburg-Landau-Gor'kov theory, and experimentally, by electron tunnelling. An attempt to generalize the Ginzburg-Landau-Gor'kov theory to cope with the case when ε0/kT ≫ 1 is then indicated. In this phenomenological theory, the normalized gapε(H)/ε(0) is taken as an order parameter ω, and the free energy is assumed to contain a term in ξ02|∇ω|2, as well as a free energy density f(ω) and magnetic energy κ(ω)H2. Some success is found.