Microscopic theory of weakly coupled superconducting multilayers in an   external magnetic field
  We present the first fully microscopic, self-consistent, and self-contained theory of superconducting weakly coupled periodic multilayers with tunnel barriers in the presence of externally applied parallel magnetic fields, in the local Ginzburg-Landau regime. We solve a nontrivial mathematical problem of a microscopic derivation and exact minimization of the free-energy functional. In the thin-layer limit that corresponds to the domain of validity of the phenomenological Lawrence-Doniach model, our physical results strikingly contrast with those of our predecessors. In particular, we completely revise previous calculations of the lower critical field and refute the concept of a triangular Josephson vortex lattice. We show that Josephson vortices penetrate into all the barriers simultaneously and form peculiar structures that we term ''vortex planes''. We calculate the superheating field of the Meissner state and predict hysteresis in the magnetization. In the vortex state, the magnetization exhibits distinctive oscillatory behavior and jumps due to successive penetration of the vortex planes. We prove that the vortex-plane penetration and pinning by the edges of the sample cause the Fraunhofer pattern of the critical Josephson current. We calculate the critical temperature and the upper critical field of infinite (along the layers) multilayers. For finite multilayers, we predict a series of first-order phase transitions to the normal state and oscillations of the critical temperature versus the applied field. Finally, we discuss some theoretical and experimental implications of the obtained results.   PACS numbers: 74.50.+r, 74.80.Dm 
Sergey V. Kuplevakhsky (Kharkov State University, Ukraine)