Campbell penetration in the critical state of type-II superconductors

TL;DR

This paper investigates how ac magnetic signals penetrate type-II superconductors in the critical state, revealing that flux penetration behaves regularly despite the vanishing pinning potential curvature.

Contribution

It introduces a microscopic approach to flux penetration in the critical state, refining the understanding of Campbell penetration depth in superconductors.

Findings

Flux penetration remains regular in the critical state.

Campbell length diverges when pinning potential curvature vanishes.

Microscopic pinning force expression clarifies flux behavior.

Abstract

The penetration of an $ac$ magnetic signal into a type II superconductor residing in the Shubnikov phase depends on the pinning properties of Abrikosov vortices. Within a phenomenological theory, the so-called Campbell penetration depth $\lambda_{\rm \scriptscriptstyle C}$ is determined by the curvature $\alpha$ at the bottom of the effective pinning potential. Preparing the sample into a Bean critical state, this curvature vanishes and the Campbell length formally diverges. We make use of the microscopic expression for the pinning force density derived within strong pinning theory and show how flux penetration on top of a critical state proceeds in a regular way.