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My first recollection of superconducting clusters is based on work by Guy Deutscher and coworkers in Tel Aviv, where they probed certain random arrays of microscopic metallic particles. Coming to Israel soon after, I mentioned the amusing properties of “wire networks”, where some superconducting threads (simple loops, or connected periodic networks) are exposed to a magnetic field.
Some of the fundamental phenomena of superconductivity are observed in samples with a nontrivial topology. The purpose of this book is to assemble evidence ranging from experimental physics to pure mathematics that supports this assertion. The task is not easy. The different communities represented in the book have very different perspectives. They often even talk in different languages. But we feel...
The technology of the second half of the XX century was largely based on the applications of the quantum physics of the solid state, which explains the electronic properties of matter. Technology of the XXI century will surely be based on the macroscopic quantum properties of matter, that is to say, on the coherent macroscopic states of physical systems, some of their best known examples are the laser, superfluidity...
This is a survey on [HHOO] and further developments of the theory [He4]. We explain in detail the origin of the problem in superconductivity as first presented in [BeRu], recall the results of [HHOO] and explain the extension to the Dirichlet case. As illustration of the theory, we detail some semi-classical aspects and give examples where our estimates are sharp.
We have analyzed the effect of connectivity on flux confinement by studying the normal/superconducting phase boundaries Tc(H) in structures with different topologies. Three different types of nanostructured superconductors are considered: individual nanoplaquettes (loops, dots), one- and two-dimensional clusters of plaquettes, and finally huge arrays of nanoplaquettes (e.g. antidot lattices...
We discuss the conditions and the positions where the order parameter vanishes in a multiply connected sample. The first sections are extensions of the de Gennes-Alexander formalism, but most of the chapter deals with samples of finite width. There are several surprising predictions, e.g.: a vortex can be much thinner than the coherence length, and its position may radically change with the fluxoid...
Persistent currents in superconducting rings were predicted in the early 1950’s [17], and then experimentally observed in the early 1960’s [12] and the notes that follow it). Moreover, it was shown that they are extremely stable, lasting for years!
There has been much activity recently involving an examination of the phase transition between the normal and superconducting state when a sample is subjected to an applied magnetic field. The curve relating critical temperature to applied field marking this transition has in particular been the subject of numerous studies by experimental physicists, see e.g. [17] or [5]. In this article, we will...
A numerical method for the solution of the time-dependent Ginzburg-Landau equations is detailed. The method is based on the popular technique of gauge invariant variables. Extension of the method to multiply connected domains is addressed. An implementation of the method is made available through the Web.
We discuss formation of vortices and antivortices in field theory systems. We first describe conventional models, where such topological defects are produced either via thermal fluctuations, or via a non-equilibrium mechanism, known as the Kibble mechanism, during a phase transition. We then describe a new mechanism, recently proposed by us, where defect-antidefect pairs are formed due to strong oscillations,...
Although it is only in the very simplest cases that the order parameter of a superfluid or superconductor can be regarded literally as a Schrödinger wave function, it is quite generally “very like” one, and thinking of it in this way can often be quite helpful to one’s intuition, particularly in cases involving internal degrees of freedom. In this chapter I shall briefly sketch the basis for this...
In classical electrodynamics, the scalar and vector potentials are mathematical artifacts, designed to simplify calculation, without any real physical significance. However, in quantum theory this is no longer true; potentials enter Schrödinger’s equation in an intimate way, and can produce directly observable effects. As far as I am aware, this was first pointed out by Ehrenberg and Siday [1] in...
Inhomogeneous superconductors, made up of superconducting and non superconducting regions, or of regions having different critical temperatures, have properties that may differ considerably from those of ideally homogeneous superconductors. We review here some examples of interest, such as superconductor/ normal metal contacts, superconducting networks embedded in insulating matrices, and granular...
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