Current-carrying states in superconductor/insulator and   superconductor/semiconductor superlattices in the mesoscopic regime
  We discuss some of the basic theoretical aspects of current-carrying states in superconducting superlattices with tunnel barriers in the mesoscopic regime, when the superconducting layer thickness is small compared to the BCS coherence length but large compared to the atomic scale. We establish the necessary conditions for the observation of the classical Josephson effect (with sinusoidal current-phase dependence) and derive self-consistent analytical expressions for the critical Josephson current. These expressions are proportional to an additional small factor and have unusual temperature dependence as compared with the single-junction case. For certain parameter values, the superconducting gap exhibits an exponential decrease due to pair-breaking effect of the supercurrent. The supercurrent can completely destroy the superconductivity of the system above a certain characteristic temperature (lower than the transition temperature of individual layers). In this paper, we also study the effect of intrabarrier exchange interactions. We show that this effect is strongly enhanced compared with the single- junction case and can manifest itself in an exponential decrease of the critical temperature. 
S. V. Kuplevakhsky, A.V. Naduev,(1) and S. V. Naydenov (2) (1- Kharkov   State University, Ukraine, 2-Institute for Single C...