Electronic Structure of the Intermediate State in Type-I Superconductors

The quasiparticle wave functions and the energy-eigenvalue equations of the intermediate state in extreme type-I superconductors are calculated for the full range of the excitation spectrum. A WKBJ method of solving the Bogoliubov equations at any temperature below $T_c$ is used. The periodicity of the pair potential leads to Bloch-type wave functions and a band structure of the energy spectrum for fixed momenta parallel to the phase boundaries. The magnetic field has an effect on the quasiparticle energies only by its influence on the structural and thermodynamic properties of the system. The width of the normal regions, and an effective variation length summing up the space dependence of the pair potential, are the variational parameters of the theory. From the general eigenvalue equations explicit energy spectra are obtained for simplified models of the pair potential.