Two-Fluid Description of Two-Band Superconductors

We present a systematic study of the response properties of two-band (multi-gap) superconductors with spin-singlet (s-wave) pairing correlations, which are assumed to be caused by both intraband (λii, i=1,2) and interband (λ12) pairing interactions. In this first of three planned publications we concentrate on the properties of such superconducting systems in global and local thermodynamic equilibrium, the latter including weak perturbations in the stationary long-wavelength limit. The discussion of global thermodynamic equilibrium must include the solution (analytical in the Ginzburg–Landau and the low temperature limit) of the coupled self-consistency equations for the two energy gaps Δi(T), i=1,2. These solutions allow one to study non-universal behavior of the two relevant BCS-Mühlschlegel parameters, namely the specific heat discontinuity \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\varDelta C/C_{\rm N}$\end{document} and the zero temperature gaps \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\varDelta_{i}(0)/\pi k_{\rm B}T_{\rm c}$\end{document}, i=1,2. The discussion of a local equilibrium situation includes the calculation of the supercurrent density as a property of the condensate, and the calculation of both the specific heat capacity and the spin susceptibility as properties of the gas of thermal excitations in the spirit of a microscopic two-fluid description. A behavior in the temperature dependences of the gaps and all these local response functions, typical for two-band superconductors is analysed particularly for very small values of the interband pair-coupling constant λ12.