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 $\eta$, which prevents us from obtaining a {\it true} upper critical field $H_{\mathrm{c}2}$ 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 $H_{\mathrm{c}2}$ due to field dependence of ${\xi }_v$. This may revitalize the single-band Kogan model in combination with a universal function $\eta (\gamma ,B,H_{\mathrm{c}2})$ instead of a constant $\eta$.