Two-dimensional arrays of superconducting strips as dc magnetic metamaterials

TL;DR

This paper theoretically analyzes the magnetic response of 2D superconducting strip arrays, deriving their effective permeability and demonstrating how array geometry influences magnetic anisotropy, with potential applications in dc magnetic metamaterials.

Contribution

It provides analytical and numerical insights into the magnetic properties of superconducting strip arrays, highlighting the impact of array geometry on anisotropy.

Findings

Effective permeability exhibits large anisotropy depending on array configuration.

Hexagonal arrays achieve greater magnetic anisotropy than rectangular arrays.

Finite Pearl length effects are considered in numerical calculations.

Abstract

We theoretically investigate the magnetic response of two-dimensional arrays of superconducting strips, which are regarded as essential structures of dc magnetic metamaterials. We analytically obtain local distributions of the magnetic field for the ideal complete shielding state (i.e., $\Lambda/w\to 0$, where $2w$ is the strip width, $\Lambda=\lambda^2/d$ is the Pearl length, $\lambda$ is the London penetration depth, and $d$ is the strip thickness), and derive effective permeability by averaging the local field distributions. We also perform numerical calculations for a realistic case, taking finite $\Lambda/w>0$ into account. We investigate two types of strip arrays: a rectangular array and a hexagonal array. The resulting effective permeability has large anisotropy that depends on the dimensions and arrangement of the superconducting strips, and the hexagonal array is found to be more advantageous for obtaining large anisotropy than the rectangular array.