Entropy and Spin Susceptibility of s-wave Type-II Superconductors near $H_{c2}$

A theoretical study is performed on the entropy $S_{\mathrm{s}}$ and the spin susceptibility ${\chi }_{\mathrm{s}}$ 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 $[S_{\rm s}(T,B)-S_{\rm s}(T,0)]/[S_{\rm n}(T)-S_{\rm s}(T,0)]=1-\alpha_{S}(1-B/H_{c2})\approx (B/H_{c2})^{\alpha_{S}}$,forexample,where$B$ is the average flux density and $S_{\mathrm{n}}$ 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 $S_{\mathrm{s}}(B)$ and ${\chi }_{\mathrm{s}}(B)$ near T=0 are convex downward (upward) in the dirty (clean) limit, deviating substantially from the linear behavior $\propto B\mathrm{/}{H}_{c2}$. The specific-heat jump at $H_{c2}$ also shows fairly large mean-free-path dependence.