Torque theory of anisotropic superconductors with no phenomenological parameter in determining vortex core size

The contribution of the vortex core has been taken into account properly in constructing a torque theory for multiband superconductors. We employ the prescription for describing the internal magnetic field in the vortex lattice by Hao et al. and by Yaouanc et al. to derive a torque formula as a natural extension of a preceding London theory. In marked contrast with the preceding model, our formula does not contain a phenomenological parameter $\eta$, which prevents us from obtaining a 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 $\eta$. DOI: http://dx.doi.org/10.1103/PhysRevB.83.184518 ©2011 American Physical Society