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ORAL CONTRIBUTIONS
Penetration of magnetic field in type II superconductors studied by
time dependent Ginzburg-Landau equation
Isaias G. de Oliveira
Departamento de Física, Universidade Federal Rural de Rio de Janeiro BR-465, km 7, CEP
2389-000, Seropedica, Rio de Janeiro, Brazil
The time-dependent Ginzburg-Landau (GL) equation is solved numerically for type-II
superconductors using the finite element method [1][2]. The size of the mesoscopic
sample, the GL parameter, and the applied magnetic field have a marked influence on
the petration of the magnetic field, the magnetic vortex distribution and the vortex
dynamics. In this workshop I will present different behaviors of magnetic field
penetration in superconductors:
1. For large sample (Lx = 100λ and Ly = 50λ) with ĸ = 4, and subjected to an
uniform magnetic field H = 1.5H c2 . The initial penetration of magnetic field
presents usual penetration behavior. After few times the penetration of magnetic
field presents a new behavior, when so, appear small structures: the magnetic
fingers. They increace until there exist nucleation of vortices on the top of these
fingers. The magnetic fingers structure are destroyed however it returns to
increace again. The vortices nucleated are driven to the centre of the sample
pushed by the giant vortices fingers.
2. For a mesoscopic superconductor square with slit and hole [3]. In this case I
have studied the vortices penatration for different values of _ and applied
magnetic field. For soft type II superconductors (for instance, ĸ = 3) there are a
penatration of multivortices and the system find the stability so fast. Otherwise,
for extremely hard superconductors (for instance, ĸ = 20), there are nucleations
of multivortices and also appear giants vortices in the corners of the hole. From
these giants vortices in the corners multivortices are nucleated.
3. Presence of defects. To illustrate the dynamics of vortices entering a defect in a
square shaped type-II superconductor, I will present the time evolution of
vortices for different values of ĸ and applied magnetic field. The applied field is
kept constant, after the system arrive in a stable configuration the magnetic field
is inverted. By this time we can see three simultaneous effects: penetration of
anti-vortices, expelling of vortices and annihilation of vortex and anti-vortex.
[1] The software Comsol 3.5a and MatLab have been used for numerical calculations.
[2] T.S. Alstrøm et al., Acta Appl Math DOI 10.1007 , August 2010.
[3] E. H. Brandt, Journal of Low Temperature Physics, Vol. 130, Nos. 3/4,
February 2003
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