2D barrier in a superconducting niobium square Miryam R. Joya, Edson Sardella, and J. Barba-ortega Citation: AIP Conference Proceedings 1627, 37 (2014); doi: 10.1063/1.4901654 View online: http://dx.doi.org/10.1063/1.4901654 View Table of Contents: http://scitation.aip.org/content/aip/proceeding/aipcp/1627?ver=pdfcov Published by the AIP Publishing Articles you may be interested in High field vortex matching effects in superconducting Nb thin films with a nanometer-sized square array of antidots J. Appl. Phys. 108, 053906 (2010); 10.1063/1.3480812 Characteristics of Zr-based single- and multiple-barrier superconducting tunnel junctions Appl. Phys. Lett. 88, 212504 (2006); 10.1063/1.2204454 Josephson junctions with nearly superconducting metal silicide barriers Appl. Phys. Lett. 87, 222511 (2005); 10.1063/1.2137992 Pinning phenomena in a superconducting film with a square lattice of artificial pinning centers Appl. Phys. Lett. 84, 5371 (2004); 10.1063/1.1767278 Verification of the theory of Brownian motion of a particle through a potential barrier in a viscous medium during experimental study of dislocation acoustic relaxation in normal and superconducting niobium Low Temp. Phys. 23, 922 (1997); 10.1063/1.593492
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2D Barrier in a Superconducting Niobium Square Miryam R. Joya 1,a) Edson Sardella 2,3,b) and J. Barba-ortega1,c) 1
Departamento de Física, Universidad Nacional de Colombia, carrera 30 # 45-03, Bogotá 1149 Colombia 2 Departamento de Física, Universidade Estadual Paulista, Caixa Postal 473, Baurú-SP, Brazil 3 Universidade Estadual Paulista, IPMet-Instituto de Pesquisas Meteorológicas, CEP 17048-699 Bauru--SP, Brazil a)
[email protected] b)
[email protected] c)
[email protected] Abstract. The presence of barriers changes the vortex structure in superconducting Nb square in presence of a uniform applied magnetic field. The Cooper pair configurations in a mesoscopics superconducting square of Nb with a barrier are calculated within the nonlinear Ginzburg Landau equations. We predict the nucleation of multi-vortex states into the sample and a soft entry of the magnetic field inside and around into the barrier. A novel and non-conventional vortex configurations occurs at determined magnetic field.
INTRODUCTION For a bulk type 2 and/or type 1.5 superconductor, the magnetic field can penetrate in the form of vortices, each carrying one single fluxoid, arranged in a hexagonal lattice. This so-called mixed state or Shubnikov state and takes place between the first and the second critical magnetic fields. For mesoscopic samples the superconducting properties as well as the vortex configurations, can present new and very interesting properties. The superconducting properties of samples with structured anti-pinning cores have attracted over the past years [1, 2]. Motivated by engineered advances, superconducting materials with different arrays of dots or anti-dots revealed a rich diversity of interesting phenomena. The possibility of controlling the properties of the superconducting condensate, i.e. vortex matter, critical currents and fields has made from mesoscopics superconductors one of the favorite experimental and theoretical systems for studies [3,5].It was observed that when the pinning centers are placed closer, the vortex profile depend on their density and the pinning size [2].also due to the influence of vortex structures in Niobium samples, a transition from Shubnikov like vortex lattice to vortex shell structures take place at interstitial sites. In previous works the authors of this paper studied the effects associated to the pinning force of both a point-like and circular defect on the vortex configuration, thermodynamical properties and the vortex entry and expulsion fields in a very thin disk, the authors found that due to vortex-defect attraction, the vortices always are found to be sitting on the pinning center position [6,7]. In addition, they analyzed the superconducting condensate in a superconducting nano-square with a central symmetrical square pillar of different, a novel vortex configurations as a function of magnetic field was found [8]. Berdiyorov studied the phase boundaries for square samples containing several anti-dots in the presence of a uniform perpendicular magnetic field, they found that the phase of these structures reveals an oscillatory behavior caused by the formation of vortex configurations in these pinning anti-dots [9]. Baelus found that due to the interplay between the vortex-vortex repulsion and the vortex-defect interaction, the vortex does not enter or leave the sample through the surface defect. With increasing field, the number of vortices simultaneously entering the sample also depends on the presence and the positions of the surface defects [10]. Now, in this work in the framework of non-lineal time dependent Ginzburg Landau equations we calculated the magnetization, free energy and Cooper pair density for a thin Nb superconducting square sample of area S u S S S 64[ 2 (0) with a rectangular and asymmetrical square tower of cross section area
aub
Sd
12[ 2 (0) in presence of an external magnetic field H e applied perpendicular to its surface.
Electroceramics XIV Conference AIP Conf. Proc. 1627, 37-41 (2014); doi: 10.1063/1.4901654 © 2014 AIP Publishing LLC 978-0-7354-1264-4/$30.00
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THEORETICAL METHOD In the time dependent Ginzburg Landau approach, the vortices are spontaneously nucleated at the surface and then penetrate inside the sample. After that, they will accommodate into an equilibrium configuration in order to minimize the free energy. We study the properties of a thin mesoscopic superconducting square with small rectangular defect on its surface. For this sample the external magnetic field is applied along the z axis (see Figure 1). The time dependent Ginzburg-Landau (TDGL) equations for isotropic superconductors which govern the superconductivity order parameter and the vector potential in the zero electric potential gauge are given by: [11-14]:
w< 2 D 2 < (1 T )( < 1)< wt wA (1 T ) Re(1 T )(
