Narrow Results

The free energy, non-gradient terms of the Ginzburg–Landau (GL) expansion, and the jump of the specific heat of a multiband anisotropic-gap BCS superconductor are derived in the framework of a separable-kernel approximation. Results for a two-band superconductor, d-wave superconductor, and some recent models for MgB₂ are worked out as special cases of the general approach. The classical results for the GL coefficients are derived in a simple way, directly from the general expression for the free energy of a BCS superconductor.

We have analyzed what new fundamental information on the properties of superconductors can be obtained by systematic investigation of the Bernoulli effect. We show that the latter is a tool to determine the effective mass of Cooper pairs, the volume density of charge carriers, the temperature dependence of the penetration depth and the condensation energy. To this end, the theoretical results for disordered and anisotropic-gap superconductors are systematized. For clean anisotropic-gap superconductors we present a simple derivation of the temperature dependence of the penetration depth.

Within the weak-coupling BCS scheme we derive a general form of the coefficients in the Ginzburg–Landau expansion of the free energy of a superconductor for the case of a Fermi level close to a Van Hove singularity (VHS). A simple expression for the influence of the VHS on the specific heat jump is then obtained for the case where gaps for different bands are distinct but nearly constant at the corresponding sheets of the Fermi surface.