Phase-dependent energy spectrum in Josephson weak links

Abstract

The quasiparticles energy spectrum in clean Josephson weak links is studied theoretically. The density of states (DOS) is calculated for various situations: s-wave or d-wave symmetry of the order parameter in the superconducting electrodes, the barrier consisting of a normal or a monodomain ferromagnetic metal. The number of peaks in DOS, corresponding to the Andreev bound states, in the anisotropic d-wave case can be greater than in the isotropic s-wave case, provided that the barrier acceptance angle is not too small. Energy levels of the bound states are explicitly obtained as a function of the barrier thickness and exchange field and in the d-wave case of the orientation of the crystalline axes of the electrodes. The spectra are strongly influenced by the macroscopic phase difference at the link.