Variational approach to vortex penetration and vortex interaction

Abstract

A variational calculation for vortex penetration is presented. Variational trial functions for the Meissner state are combined with variational functions for a vortex near the surface. The latter is based on Clem's trial solutions for a vortex in bulk, which were adapted to include surface effects through consideration of an image vortex. Three variational parameters are considered, corresponding to the effective coherence length of the vortex, the effective penetration length for the Meissner currents, and the value of the order parameter at the surface. The results show that the last two variational parameters are independent of vortex position. Explicit calculations are presented for several $\kappa$ values. The energy barrier for vortex penetration is shown to be in good agreement with full numerical calculations of the Ginzburg--Landau equations. We consider the variation of the magnetic flux carried by a vortex as it gets inside the superconductor and agreement with known experimental and theoretical results is obtained. The model was extended to calculate the force between two vortices, and the results show that the force goes to zero as the pair comes close to the surface. This result can be of interest for the study of the melting of the vortex lattice and for vortices confined in mesoscopic superconductors. The variational approach can be very helpful for intermediate $\kappa$ values when numerical calculations become computationally demanding because it provides manageable expressions for all physically relevant quantities.

11 pages, 8 figures

References in corpus (7)

• The Flux-Line Lattice in Superconductors
• Non-Quantized Penetration of Magnetic Field in the Vortex State of Superconductors
• From vortex molecules to the Abrikosov lattice in thin mesoscopic superconducting disks
• Hysteresis in mesoscopic superconducting disks: the Bean-Livingston barrier
• The surface barrier in mesoscopic type I and type II superconductors
• The ac magnetic response of mesoscopic type II superconductors
• Anisotropic ac dissipation at the surface of mesoscopic superconductors

Cited by in corpus (8)

• (Giant) Vortex - (anti) vortex interaction in bulk superconductors: The Ginzburg-Landau theory
• Vortex-vortex interaction in thin superconducting films
• Lateral imaging of the superconducting vortex lattice using Doppler-modulated scanning tunneling microscopy
• Coleman-Weinberg Abrikosov-Nielsen-Olesen strings
• Vortex penetration and flux relaxation with arbitrary initial conditions in non-ideal and ideal superconductors
• Mathematical model of vortex penetration phenomenon
• Interaction between multi components vortices at arbitrary distances using a variational method in the Ginzburg-Landau theory
• Vortices in a Ginzburg Landau Theory of Superconductors with Nematic Order