A theoretical study is performed on the entropy $S_{ \rm s}$ and the spin susceptibility $\chi_{ \rm s}$ near the upper critical field $H_{ c2}$ of s-wave type-II superconductors with arbitrary impurity concentrations. The changes of these quantities through $H_{ c2}$ may be expressed as $[S_{ \rm s}(T,B)-S_{ \rm s}(T,0)]/[S_{ \rm n}(T)-S_{ \rm s}(T,0)]=1-\alpha_{ S}(1-B/H_{ c2})\approx (B/H_{ c2})^{ \alpha_{ S}}$, for example, where $B$ is the average flux density and $S_{ \rm n}$ denotes entropy in the normal state. It is found that the slopes $\alpha_{ S}$ and $\alpha_{ \chi}$ at T=0 are identical, connected directly with the zero-energy density of states, and vary from 1.72 in the dirty limit to $0.5\sim 0.6$ in the clean limit. This mean-free-path dependence of $\alpha_{ S}$ and $\alpha_{ \chi}$ at T=0 is quantitatively the same as that of the slope $\alpha_{ \rho}(T=0)$ for the flux-flow resistivity studied previously. The result suggests that $S_{ \rm s}(B)$ and $\chi_{ \rm s}(B)$ near T=0 are convex downward (upward) in the dirty (clean) limit, deviating substantially from the linear behavior $\propto B/H_{ c2}$. The specific-heat jump at $H_{ c2}$ also shows fairly large mean-free-path dependence.
Categories: cond-mat.supr-con