Specific heat and low-lying excitations in the mixed state for a type II superconductor

Low temperature behavior of the electronic specific heat $C(T)$ in the mixed state is by the self-consistent calculation of the Eilenberger theory. In addition to $\gamma T$-term ($\gamma$ is a Sommerfeld coefficient), $C(T)$ has significant contribution of $T^2$-term intrinsic in the vortex state. We identify the origin of the $T^2$-term as (i) V-shape density of states in the vortex state and (ii) Kramer-Pesch effect of vortex core shrinking upon lowering $T$. These results both for full-gap and line node cases reveal that the vortex core is a richer electronic structure beyond the normal core picture.