Related papers: Minimizers of the Lawrence-Doniach energy in the s…
We consider the Lawrence-Doniach model for layered superconductors, in which stacks of parallel superconducting planes are coupled via the Josephson effect. We assume that the superconductor is placed in an external magnetic field oriented…
We study minimizers of the Lawrence--Doniach energy, which describes equilibrium states of superconductors with layered structure, assuming Floquet-periodic boundary conditions. Specifically, we consider the effect of a constant magnetic…
We analyze minimizers of the Lawrence-Doniach energy for three-dimensional highly anisotropic superconductors with layered structure. For such a superconductor occupying a bounded generalized cylinder in $\mathbb{R}^3$ with equally spaced…
We analyze minimizers of the Lawrence-Doniach energy for layered superconductors occupying a bounded generalized cylinder, $ \Omega\times[0,L]$, in $\mathbb{R}^3$, where $\Omega$ is a bounded simply connected Lipschitz domain in…
We solve the problem of exact minimization of the Lawrence-Doniach (LD) free-energy functional in parallel magnetic fields. We consider both the infinite in the layering direction case (the infinite LD model) and the finite one (the finite…
For the first time, we obtain the complete and exact analytical solution of the Lawrence-Doniach model for layered superconductors in external parallel magnetic fields. By solving a nontrivial mathematical problem of exact minimization of…
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…
We study minimizers of the two-dimensional Ginzburg-Landau energy with applied magnetic field, between the first and second critical fields. In this regime, minimizing configurations exhibit densely packed hexagonal vortex lattices, called…
The study of singular perturbations of the Dirichlet energy is at the core of the phenomenological-description paradigm in soft condensed matter. Being able to pass to the limit plays a crucial role in the understanding of the…
We report on a Monte Carlo study of the lowest-Landau-level limit of the Lawrence-Doniach model for a layered superconductor. We have studied order parameter correlation functions for indications of the broken translational symmetry and the…
The present paper is an extension of 'cond-mat/0312673'. The construction of a hybrid discrete-continuous model of layered superconductors is presented. The model bases on the classic Lawrence-Doniach scenario with admitting, however,…
The interaction of an edge dislocation made of half the superconducting plane with a magnetic interlayer vortex is considered within the framework of the Lawrence-Doniach model with negative as well as positive Josephson interlayer…
The present paper develops the ideas introduced in {\em cond-mat/0312673}. The construction of a hybrid discrete-continuous model of layered superconductors is briefly presented. The model bases on the classic Lawrence-Doniach scenario with…
We study energy minimizers of the Ginzburg-Landau (GL) free energy, a fundamental model of superconductivity. We address the high-$\kappa$ regime, the regime of a large GL parameter, in which energy minimizers exhibit vortex structures…
We study a variational model which combines features of the Ginzburg-Landau model in 2D and of the Mumford-Shah functional. As in the classical Ginzburg-Landau theory, a prescribed number of point vortices appear in the small energy regime;…
We analyze a mean field model for $3$d anisotropic superconductors with a layered structure, in the presence of a strong magnetic field. The mean field model arises as the $Gamma$-limit of the Lawrence-Doniach energy in certain regimes. A…
Many superconducting materials are composed of weakly coupled conducting layers. Such a layered structure has a very strong influence on the properties of vortex matter in a magnetic field. This review focuses on the properties of the…
We study a $(1+1)$-dimensional semi-discrete random variational problem that can be interpreted as the geometrically linearized version of the critical $2$-dimensional random field Ising model. The scaling of the correlation length of the…
The equivalence between the Lawrence-Doniach model for films of extreme type-II layered superconductors and a generalization of the back-scattering model for spin-1/2 electrons in one dimension is demonstrated. This fermion analogy is then…
We consider a Ginzburg-Landau type energy with a piecewise constant pinning term $a$ in the potential $(a^2 - |u|^2)^2$. The function $a$ is different from 1 only on finitely many disjoint domains, called the {\it pinning domains}. These…