Field Dependence of Electronic Specific Heat in Two-Band Superconductors

The vortex structure is studied in light of MgB${}_2$ theoretically based on a two-band superconducting model by means of Bogoliubov-de Gennes framework. The field dependence of the electronic specific heat coefficient $\gamma (H)$ is focused. The exponent $\alpha$ in $\gamma (H)\propto H^{\alpha }$ is shown to become smaller by adjusting the gap ratio of the two gaps on the major and minor bands. The observed extremely small value $\alpha \sim 0.23$ could be explained reasonably well in this two-band model with the gap ratio $\sim 0.3$.