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

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 $η$, which prevents us from obtaining a {\it true} upper critical field $H_{\rm c2}$ by analyzing an experimental torque curve. The parameter $η$ was originally introduced to take care of the uncertainty in determining the vortex core size $ξ_v$. Furthermore, we reveal that the $η$ value is universally scaled by anisotropy $γ$, magnetic field $B$, and $H_{\rm c2}$ due to field dependence of $ξ_v$. This may revitalize the single-band Kogan model in combination with a universal function $η(γ, B, H_{\rm c2})$ instead of a constant $η$.

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