Magnetic flux density and the critical field in the intermediate state of type-I superconductors

TL;DR

This paper investigates the magnetic flux structure and critical field in the intermediate state of high purity type-I superconductors, revealing that the critical field can be significantly lower than previously thought and introducing a new theoretical model.

Contribution

It presents a novel theoretical model that explains the properties of the intermediate state and allows for quantitative determination of key superconducting parameters.

Findings

Critical field in the intermediate state can be as low as 40% of the thermodynamic critical field.

Flux density in normal domains can be less than the critical field, contradicting previous paradigms.

The model provides new insights and quantitative tools for understanding superconductor properties.

Abstract

To address unsolved fundamental problems of the intermediate state (IS), the equilibrium magnetic flux structure and the critical field in a high purity type-I superconductor (indium film) are investigated using magneto-optical imaging with a 3D vector magnet and electrical transport measurements. The least expected observation is that the critical field in the IS can be as small as nearly 40% of the thermodynamic critical field $H_c$. This indicates that the flux density in the \textit{bulk} of normal domains can be \textit{considerably} less than $H_c$, in apparent contradiction with the long established paradigm, stating that the normal phase is unstable below $H_c$. Here we present a novel theoretical model consistently describing this and \textit{all} other properties of the IS. Moreover, our model, based the rigorous thermodynamic treatment of observed laminar flux structure in a tilted field, allows for a \textit{quantitative} determination of the domain-wall parameter and the coherence length, and provides new insight into the properties of all superconductors.