Related papers: Vortex Lattices and the Bogoliubov-De Gennes Equat…
We consider the Bogolubov-de Gennes equations giving an equivalent formulation of the BCS theory of superconductivity. We are interested in the case when the magnetic field is present. We (a) discuss their general features, (b) isolate key…
A self-consistent Bogoliubov deGennes theory of the vortex lattice state in a 2D strong type-II superconductor at high magnetic fields reveals a novel quantum mixed state around the semiclassical Hc2, characterized by a well-defined…
The Ginzburg-Landau equations play a key role in superconductivity and particle physics. They inspired many imitations in other areas of physics. These equations have two remarkable classes of solutions -- vortices and (Abrikosov) vortex…
In this paper, we present a method to construct the eigenspace of the normal-state electrons moving in a 2D square lattice in presence of a perpendicular uniform magnetic field which imposes (quasi)-periodic boundary conditions for the wave…
We use a Bogoliubov-de Gennes (BdG) formulation to describe a single vortex in a neutral fermionic gas. It is presumed that the attractive pairing interaction can be arbitrarily tuned to exhibit a crossover from BCS to Bose-Einstein…
We study the interplay of vortices and disorder in a two-dimensional disordered superconductor at zero temperature described by the Bogoliubov-de Gennes (BdG) self-consistent formalism for lattices of sizes up to $100\times100$ where the…
We prove existence of Abrikosov vortex lattice solutions of the Ginzburg-Landau equations in two dimensions, for magnetic fields larger than but close to the first critical magnetic field.
Following Bogomolnyi's classical treatment of vortices, we develop a method for finding rigorous lower bounds to the Landau-Ginzburg free energy describing unconventional superconductors in the absence of external magnetic fields. This…
Bogoliubov-de Gennes theory is used to investigate the effect of the size of a superconducting square on the vortex states in the quantum confinement regime. When the superconducting coherence length is comparable to the Fermi wavelength,…
The Gross-Pitaevskii-type equation is solved for the charge Bose liquid in the external magnetic field at zero temperature. There is a vortex lattice with locally broken charge neutrality. The boson density is modulated in real space and…
We consider the vortex matter in a three-dimensional two-component superconductor with individually conserved condensates with different bare phase stiffnesses in a finite magnetic field, such as the projected superconducting state of…
We are going to analyze the nucleation of vortices in a thin mesoscopic superconducting disk. The Gibbs free energy from London model is formulated. This energy function, with an arbitrary configuration of vortices, is assoicated with the…
We study the linearized stability of n-vortex solutions of the magnetic Ginzburg-Landau (or Abelian-Higgs) equations. We prove that the fundamental vortices (n=1,-1) are stable for all values of the coupling constant, k, and we prove that…
We prove existence of Abrikosov vortex lattice solutions of the Ginzburg-Landau equations of superconductivity, with multiple magnetic flux quanta per a fundamental cell. We also revisit the existence proof for the Abrikosov vortex…
It is shown that bound state solutions of the one dimensional Bogoliubov-de Gennes (BdG) equation may exist when the Fermi velocity becomes dependent on the space coordinate. The existence of bound states in continuum (BIC) like solutions…
We deal with a type I superconductor in a constant external magnetic field. We obtain the BCS-Bogoliubov gap equation with external magnetic field and apply the implicit function theorem to it. We show that there is a unique magnetic field…
It is generally accepted that vortex core is charged, what illustrates that even in stationary superconductors electric field may be present. Vortex structure and other properties of superconductors are usually calculated in the framework…
Our study sample is a superconducting bi-dimensional octagon with different boundary conditions immersed in a magnetic external field H. The boundary conditions are simulated by considering different values of the deGennes extrapolation…
We examine the one-dimensional Gross-Pitaevskii lattice at zero temperature in the presence of uncorrelated disorder. We obtain analytical expressions for the thermodynamic properties of the ground state field and compare them with…
A method is presented to solve the Bogoliubov-de Gennes equations with arbitrary distributions of vortices. The real-space Green's function approach based on Chebyshev polynomials is complemented by a gauge transformation which allows one…