Effective magnetic penetration depth in superconducting cylinders and spheres with highly anisotropic electrodynamics

TL;DR

This paper derives the effective magnetic penetration depth and microwave surface impedance for highly anisotropic layered superconductors in specific geometries, extending the analysis to lossy and highly anisotropic conductors, with exact solutions for certain limits.

Contribution

It provides analytical expressions for penetration depth and impedance in anisotropic superconductors, including special cases relevant to layered materials like cuprates.

Findings

Exact solutions for lambda_a → 0 limit.

Analytic continuation to highly anisotropic conductors.

Applicability to experiments on layered superconductors.

Abstract

Effective magnetic penetration depth and microwave surface impedance are derived for anisotropic layered superconductors in the shape of spheres and long cylinders, where the external magnetic field is applied in the plane of the highly conducting layers to induce out-of-plane screening currents. The results are extended by analytic continuation to highly anisotropic conductors and to lossy superconductors at high frequency. The electrodynamics for the general case of a superconductor or metal with arbitrary anisotropy are presented. The treatment is then specialized to layered materials with unixaxial anisotropy, in which the penetration depth for currents flowing perpendicular to the layers, lambda_c, is much greater than that for in-plane currents, lambda_a. Exact solutions are found in the limit lambda_a goes to zero, and are expected to provide an accurate representation of many experiments on cuprates and other layered superconductors, particularly on grain-aligned powders.