The London Study of Vortex States in a Superconducting Film Due to a Magnetic Dot

TL;DR

This study investigates vortex configurations in a superconducting film influenced by a magnetic dot, revealing conditions for giant vortices and single-flux vortices, with predictions on their arrangements and no spontaneous antivortex formation.

Contribution

It provides a detailed theoretical analysis of vortex states induced by magnetic dots in superconducting films, including conditions for different vortex types and their geometrical patterns.

Findings

Giant vortices occur when the dot size is small ($R .5 \xi$).

Single quantum flux vortices dominate for larger dots ($R  6 \xi$).

No spontaneous antivortex formation observed.

Abstract

Here we report a study of vortex states in a thin superconducting film with a magnetic dot grown upon it by means of a method based on London-Maxwell equations. Vortices with single quantum flux ($\Phi_0 = h c / 2 e$), giant vortices (vortices with multiple flux) as well as antivortices (vortices with negative vorticity) are taken into consideration. It turns out that giant vortices occur, when the dot's size is sufficiently smaller ($R \leq 4.5 \xi $) than the effective penetration depth $\Lambda$. In the case of a dot with sufficiently large size ($R \geq 6 \xi $), the vortices with single quantum flux dominate the vortex states. Their geometrical patterns are predicted up to seven vortices. Our calculations do not show the spontaneous appearance of antivortices.