Specific Heat of the Mixed State in Superconducting Alloys

Abstract

Based on the previous theory of superconducting alloys in magnetic fields, we made a detailed study of the specific heat of the mixed state in superconducting alloys. The jump of the specific heat at the transition from the mixed state to the normal state is explicitly calculated for various values of $\kappa$, the Ginzburg-Landau parameter. In fields just above the lower critical field $H_{c1\mathrm{}}$, we find the specific heat at lower temperature is expressed in terms of $H_{c1\mathrm{}}$ as $C_m=-\left(\frac{1}{4\pi }\right)T\left(\frac{d^2{H}_{c1\mathrm{}}}{d{T}^2}\right)B+\left(\frac{d{H}_{c1\mathrm{}}}{\mathrm{dT}}\right)\left(\frac{\partial B}{\partial T}\right),$ where $B=\left(\frac{\pi }{e}\right)n$ ($n$ being the number of flux lines per unit area), and the first term, coming from the free energy associated with a flux line, is proportional to $T$.