Magnetic flux threading a planar holed superconductor

TL;DR

This paper provides an analytical study of magnetic flux and currents in a planar superconductor with a hole, offering formulas that help understand various physical scenarios relevant for sensitive experimental applications.

Contribution

It derives simple analytical relations between flux, currents, and dipole position in a planar superconductor, extending understanding of flux screening and current behavior.

Findings

Analytical expressions for flux and currents as functions of dipole position.

Study of different physical scenarios including field cooling and slit configurations.

Results serve as benchmarks for experiments in gravimetry and dark matter detection.

Abstract

We analytically evaluate the currents in a planar-holed ideal (perfect magnetic shielding) superconductor when an axial dipole is located along the system's axis, obtaining a simple relation between the fluxoid (in this geometry, it equals the flux) threading the hole, the net current circling it, and the magnitude and position of the dipole. This expression has to be added to the basic screening equations describing the superconductor to understand the different physical situations that can appear. Thus several scenarios are studied: field and zero-field cooling cases, where the flux threading the hole is fixed; superconductors with a slit where the net current circling the hole is zero; and self-inductance case, where the flux threading the hole is only due to the screening currents. All the presented results are analytical for the axial dipole and are given as a function of the distance of the dipole from the plane of the superconductor. The obtained results can serve as a benchmark for recent and ongoing micromechanical experiments aimed at developing ultrasensitive gravimeters or applications searching for exotic spin-dependent interactions and dark matter, for example.