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 $\eta$.
Categories: cond-mat.supr-con