2 research outputs found
Keldysh technique and non-linear sigma-model: basic principles and applications
The purpose of this review is to provide a comprehensive pedagogical
introduction into Keldysh technique for interacting out-of-equilibrium
fermionic and bosonic systems. The emphasis is placed on a functional integral
representation of underlying microscopic models. A large part of the review is
devoted to derivation and applications of the non-linear sigma-model for
disordered metals and superconductors. We discuss such topics as transport
properties, mesoscopic effects, counting statistics, interaction corrections,
kinetic equation, etc. The sections devoted to disordered superconductors
include Usadel equation, fluctuation corrections, time-dependent
Ginzburg-Landau theory, proximity and Josephson effects, etc. (This review is a
substantial extension of arXiv:cond-mat/0412296.)Comment: Review: 103 pages, 19 figure
Expansion of a superconducting vortex core into a diffusive metal
Vortices in quantum condensates exist owing to a macroscopic phase coherence. Here we show, both experimentally and theoretically, that a quantum vortex with a well-defined core can exist in a rather thick normal metal, proximized with a superconductor. Using scanning tunneling spectroscopy we reveal a proximity vortex lattice at the surface of 50 nm - thick Cu-layer deposited on Nb. We demonstrate that these vortices have regular round cores in the centers of which the proximity minigap vanishes. The cores are found to be significantly larger than the Abrikosov vortex cores in Nb, which is related to the effective coherence length in the proximity region. We develop a theoretical approach that provides a fully self-consistent picture of the evolution of the vortex with the distance from Cu/Nb interface, the interface impedance, applied magnetic field, and temperature. Our work opens a way for the accurate tuning of the superconducting properties of quantum hybrids