Entropy of a Type II Superconductor in the Mixed State Close to T _c

Abstract

The entropy per unit volume of a type II superconductor in the mixed state can be written in the following form: S(T, B) = S _s (T) + ΔS(T, B), where S _s (T) is the entropy in the Meissner state [H ≦ H _cl (T)]. Using the constitutive relation between the three coordinates at equilibrium, B = B(T, H), we can write alternatively S(T, H) = S _s (T) + ƊS(T, H). Three thermal quantities can be derived from the entropy S: the specific heat at constant field C _H = C _s (T) + T[∂(ΔS)/∂T] ∥ _H , the specific heat at constant induction C _B = C _s (T) + T[∂(ΔS)/∂ T] ∣ _B , and the incremental entropy of vortices S _i = ϕ ₀ [∂(ΔS/∂B] _T (ϕ _o is the flux quantum).¹ The following thermodynamic relation holds between the terms expressing the thermal contributions of the mixed state to these quantities:

$$\frac{\partial (\Delta S)}{\partial T}{{\left| _{H}-\frac{\partial (\Delta S)}{\partial T} \right|}_{B}}=4\pi {{\left[ \frac{\partial (\Delta S)}{\partial B}\left| _{r} \right. \right]}^{2}}\frac{\partial B}{\partial H}\left| _{r} \right.\ge 0$$

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