Two-fluid description of two-band superconductors

TL;DR

This paper systematically analyzes the thermodynamic and response properties of two-band superconductors with s-wave pairing, focusing on equilibrium states, gap behavior, and local responses, highlighting non-monotonic effects for weak interband coupling.

Contribution

It provides analytical solutions for energy gaps and response functions in two-band superconductors, emphasizing the effects of interband coupling on thermodynamic and local properties.

Findings

Non-monotonic temperature dependence of gaps and response functions.

Analytical solutions for gaps in Ginzburg-Landau and low-temperature limits.

Significant effects of weak interband coupling on supercurrent and thermodynamic properties.

Abstract

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 (\lambda_{ii}, i=1,2) and interband (\lambda_{12}) 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 \Delta_i(T), i=1,2. These solutions allow to study non-universal behavior of the two relevant BCS-M\"uhlschlegel parameters, namely the specific heat discontinuity \Delta C/C_N and the zero temperature gaps \Delta_i(0)/\pi k_B T_c, 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. Non-monotonic behavior in the temperature dependences of the gaps and all these local response functions is predicted to occur particularly for very small values of the interband pair-coupling constant \lambda_{12}.