Anisotropic criteria for the type of superconductivity

TL;DR

This paper generalizes the classical superconductivity type classification criterion to anisotropic materials across all temperatures, emphasizing the ratio of upper to thermodynamic critical fields over the traditional penetration depth to coherence length ratio.

Contribution

It introduces a new criterion based on the ratio of critical fields for classifying superconductors, accounting for anisotropy and temperature variations, improving upon the traditional isotropic approach.

Findings

The ratio H_{c2}/H_c is a better classification criterion than κ=λ/ξ.

Anisotropies can significantly alter the relationship between critical fields and traditional parameters.

The classical criterion is only accurate at T_c, not at lower temperatures.

Abstract

The classical criterion for classification of superconductors as type-I or type-II based on the isotropic Ginzburg-Landau theory is generalized to arbitrary temperatures for materials with anisotropic Fermi surfaces and order parameters. We argue that the relevant quantity for this classification is the ratio of the upper and thermodynamic critical fields, $H_{c2}/H_c$, rather than the traditional ratio of the penetration depth and the coherence length, $\lambda/\xi$. Even in the isotropic case, $H_{c2}/H_c$ coincides with $\sqrt{2}\lambda/\xi$ only at the critical temperature $T_c$ and they differ as $T$ decreases, the long known fact. Anisotropies of Fermi surfaces and order parameters may amplify this difference and render false the criterion based on the value of $\kappa=\lambda/\xi$.