Electrodynamics of type-II superconductor with periodic pinning array

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Abstract

Static and dynamic distribution of the superconducting condensate order parameters and current density is studied by numerical simulation of the 2D time-dependent Ginzburg–Landau equations. The vortex flux lattice in layered type-II superconductors under magnetic field above the lower critical field is described by the order parameters. Moreover, the pinning effect has been considered in this work. The Abrikosov lattice which is hexagonal in the static case is deformed due to the size of pinning centers. The dynamical order parameters distribution shows that the vortex transport (flux flow) is conducted via diffusive motion of the so-called interstitial vortices. The trajectories for interstitial vortices with different sizes of pinning centers are shown.

Introduction

The great interest in the problem of magnetic flux pinning in type-II superconductors is associated with its relevance to technological applications of superconductivity. An important challenge in applications of type-II superconductors is achieving optimal critical currents under given magnetic fields. This requires preventing depinning of Abrikosov vortices during the formation of the resistive state under the applied current. The critical current can be significantly increased at a matching field when the number of Abrikosov flux lines is equal to the number of pinning centers. When the current exceeds the critical value, the vortices move thus inducing voltage. The dynamic behavior of the Abrikosov flux lattice is strongly influenced by the pinning array. In early experiments the distances between the pinning centers, d, were larger than magnetic penetration depth. Correspondingly the magnetic fields were mostly close to Hc1 [2], so that vortices were well isolated within the applicability range of the London approximation [3]; more recently the trend was in the direction of smaller distances between the pinning centers, approaching the coherence length ξ and consequently larger fields approaching Hc2. Two strategies were employed. The standard one is reducing d, and the second is increasing the coherence length by tuning the field towards Hc2(T) [1]. In this region the London approximation is not valid and one has to use the more appropriate time-dependent Ginzburg–Landau (TDGL) approach. In the present note we address this problem.

Section snippets

Model

The order parameter characterizing the superconducting state is calculated numerically for a periodic array of pins (i.e. “nanosolid”). The configurations of the vortex lattice under different pinning arrays (triangle, square) and different pinning center sizes are studied. In addition the trajectory of interstitial vortices are calculated. The relaxation dynamics of Abrikosov vortices in a superconductor with an electric field is described by TDGL equationτψ=ψfGL, where the dimensionless

Simulation results

We consider three different pinning arrays. The pinning locations are on a square lattice in the first case and on a triangle in the second and the third cases. The pinning center sizes are one (point) in the first and second case and nine (points) in the third case. The magnetic field h=0.4 and the electric field are applied in the y-direction for all systems. Fig. 1 shows the configuration of a static vortex lattice with a rectangular pinning array (pinning size – one point); the vortex

Conclusion

The configurations of vortex lattice above the first matching field for artificial pinning arrays are studied in this work. The vortex lattices are deformed by the pinning centers. For small pinning sizes, the vortex lattice has hexagonal symmetry wether in rectangular or triangular pinning arrays. For bigger pinning sizes (nine points), the symmetry for vortex lattices is no long hexagonal and becomes triangular. The trajectories of interstitial vortices for small size pinning arrays like a

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Cited by (1)

  • Vortex energy landscape from real space imaging analysis of YBa <inf>2</inf>Cu<inf>3</inf>O<inf>7</inf> with different defect structures

    2014, Physica C: Superconductivity and its Applications
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    In particular, we analyze the case of surface nanoindented defects. Several studies have numerically simulated vortex statics and dynamics in artificial or natural periodic arrays [17–21], here we intend to use real visualized experimental results as input data for the study, opening the possibility to study any experimental arbitrary vortex array. Although, Bitter decoration has been used to understand vortex localization of large vortex lattices and study vortex lattice symmetries [22,23], these measurements yet have never been used to semi-quantitatively determine the energies involved in the vortex array.

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