Torque Theory of Anisotropic Superconductors with No Phenomenological Parameter in determining Vortex Core Size

TL;DR

This paper develops a vortex torque theory for anisotropic multiband superconductors that eliminates the phenomenological parameter, enabling more accurate determination of the upper critical field and revealing universal scaling behavior.

Contribution

It introduces a parameter-free torque formula for anisotropic superconductors, linking vortex core size to universal functions of anisotropy, field, and critical field.

Findings

The new formula does not contain the phenomenological parameter η.

η is universally scaled by anisotropy γ, magnetic field B, and H_c2.

Revitalizes the single-band Kogan model with a universal η function.

Abstract

The contribution of vortex core has been taken into account properly in constructing a torque theory for multiband superconductors. We employ the prescription of describing internal magnetic field in the vortex lattice by Hao {\it et al.} and by Yaouanc {\it et al.} to derive a torque formula as a natural extension of a preceding London theory. In marked contrast with the preceding model, our novel formula does not contain a phenomenological parameter $\eta$, which prevents us from obtaining a {\it true} upper critical field $H_{\rm c2}$ by analyzing an experimental torque curve. The parameter $\eta$ was originally introduced to take care of the uncertainty in determining the vortex core size $\xi_v$. Furthermore, we reveal that the $\eta$ value is universally scaled by anisotropy $\gamma$, magnetic field $B$, and $H_{\rm c2}$ due to field dependence of $\xi_v$. This may revitalize the single-band Kogan model in combination with a universal function $\eta(\gamma, B, H_{\rm c2})$ instead of a constant $\eta$.