The Role of Debye Relaxation in the I-V Characteristics of SNS junctions

We investigate a mechanism for dissipation in superconductor-normal metal-superconductor (SNS) junctions related to the energy relaxation of quasiparticles due to an adiabatic flow of energy levels, similar to Debye relaxation in a gas. At small voltages, this Debye mechanism gives a contribution to the conductance which is proportional to the inelastic relaxation time τ_in, and is thus much larger than the conventional contribution to the conductance which is proportional to the elastic relation time τ_el. In this regime, I-V characteristics in SNS junctions can be expressed in terms of the density of states in the normal region of the junction ν(ε,χ), where χ is the superconducting phase difference across the junction. In junctions with broken time reversal and inversion symmetry, the density of states can have terms which are odd in the phase difference chi. This generates non-reciprocal features in the I-V characteristics which can be characterized by the parameter ν(ε,χ)- ν(ε,-χ).