Superconductivity in two-band systems with variable charge carrier density. The case of MgB2

The theory of thermodynamic properties of two-band superconductor with reduced density charge carriers is developed on the base of phonon superconducting mechanism with strong electron-phonon interaction. This theory is adapted to describe the behavior of critical temperature Tc, energy gaps Delta1, Delta2, and the relative jump of electron specific heat (Cs - Cn)/Cn in the point T = Tc along with the variation of charge carrier density in the compound MgB2 when substitutional impurities with different valence are introduced into the system. It is shown, that according to the filling mechanism of energy bands which overlap on Fermi surface, the quantities Tc, Delta1, Delta2 decrease when this compound is doped with electrons and remain constant or weakly change when the system is doped with holes. The theory qualitatively agrees with the experimental data. Also is shown that the consideration of inter- and intraband scattering of electrons on impurity potential improves this agreement.Comment: 19 pages, 6 figures, 1 table. to be published in JETP (first number 2007

Collective modes in the electronic polarization of double-layer systems in the superconducting state

Standard weak coupling methods are used to study collective modes in the superconducting state of a double-layer system with intralayer and interlayer interaction, as well as a Josephson-type coupling and single particle hopping between the layers by calculating the electronic polarization function perpendicular to the layers. New analytical results are derived for the mode frequencies corresponding to fluctuations of the relative phase and amplitude of the layer order parameters in the case of interlayer pairing and finite hopping $t$. A new effect is found for finite $k$-dependent hopping: then the amplitude and phase fluctuations are coupled. Therefore two collective modes may appear in the dynamical c-axis conductivity below the threshold energy for breaking Cooper pairs. With help of numerical calculations we investigate the temperature dependence of the collective modes and show how a plasmon corresponding to charge fluctuations between the layers evolves in the normal state.Comment: 17 pages, latex, 8 ps figure