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 the $\ensuremath{\gamma}T$-term ($\ensuremath{\gamma}$ is a Sommerfeld coefficient), $C(T)$ has a 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) the Kramer-Pesch effect of vortex-core shrinking upon lowering $T$. These results for both full-gap and line-node cases reveal that the vortex core is a richer electronic structure beyond the normal core picture.