Spectral properties of disordered superconducting planar junctions

We develop a theory of spectral properties of a planar SNS junction with a weakly-disordered normal (N) part. In the absence of disorder, the energy spectrum of the junction would be gapless. The states near the Fermi level would stem from the electron trajectories that are nearly parallel to the NS interfaces. Disorder in the normal region interrupts such "shallow" trajectories and thus leads to the formation of the spectral gap. In the quasi-ballistic limit, the magnitude of the gap is determined by the inverse scattering time, and has an unusual dependence on the phase bias across the junction. The disorder-induced gap is destroyed by a sufficiently strong magnetic field applied parallel to the junction. In the absence of spin-orbit coupling, the critical field value is the one at which the Zeeman splitting reaches the magnitude of the gap, in analogy to the Clogston-Chandrasekhar limit. A strong spin-orbit coupling makes the critical field parametrically larger.