Distribution of the magnetic field and current density in superconducting films of finite thickness

Abstract

A one-dimensional equation describing the distribution of the effective vector potential $\bar{A}(y)$ across a film width, which holds for thin ($d<\lambda$) and thick ($d>\lambda$) films alike, is derived based on the analysis of a 2D Maxwell-Londons equation for superconducting films in a perpendicular magnetic field. The validity of this equation for a finite-thickness film is verified by a numerical analysis. An approximation dependence $\bar{A}(y)$, finite (with all of its derivatives) across the entire film width, is found for films, being in the Meissner state. The flux-entry field is evaluated for a film of arbitrary thickness. An approximation expression is obtained for the distribution of the sheet current density in the mixed state of a pin-free superconducting film with an edge barrier. The latter approximation allows to estimate magnetic field concentration factor at the film edge as a function of external magnetic field and geometrical parameters of the sample.

12 pages, 10 figures

References in corpus (2)

• Magneto-optical study of magnetic flux penetration into a current-carrying high-temperature superconductor strip
• Linear Response of Thin Superconductors in Perpendicular Magnetic Fields: An Asymptotic Analysis

Cited by in corpus (5)

• Theory of Type-II Superconductors with Finite London Penetration Depth
• Asymmetric weak-pinning superconducting channels: vortex ratchets
• Strong Single-Photon Coupling in Superconducting Quantum Magnetomechanics
• Reverse-domain superconductivity in superconductor-ferromagnet hybrids: effect of a vortex-free channel on the symmetry of I-V characteristics
• Picovoltmeter for probing vortex dynamics in a single weak-pinning Corbino channel