Superconductivity in two-band systems with a variable carrier density: The case of MgB2

Abstract

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 T c , energy gaps ∆ 1 , ∆ 2 , and the relative jump of electron specific heat (C S − C N )/C N in the point T = T c along with the variation of charge carrier density in the compound MgB 2 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 T c , ∆ 1 , ∆ 2 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.

The theory of thermodynamic and magnetic properties of multi-band superconductors

“…These estimations have been made taking into account the effect of occupation of energy bands only, without consideration of the impurity scattering. The obtained results correctly reflect the transition from the two-band system to the one-band system and are in qualitative agreement with the experimental data (for details see [86,87]). The above theoretical results adequately describe the dependences which were observed during the experiment [88,89].…”

“…This technique permits to obtain the analytic solutions for the critical fields H and H (c) c2 which were obtained based on the constructed two-band theory. We use the constants of the electron-phonon interaction λ nm and µ 0 (see section 5) which correspond to MgB 2 as well as λ = v1 v2 = 0.8 (the relation of electron velocities on the difference cavities of the Fermi surface) [86]. The parameter ε defined by the declination of σ-band from two-dimensionality is taken as ε = 0.31.…”

“…Start with the system of equations for the BCS-type order parameters ∆ n (n = 1, 2) for the two-band model with the electron-phonon interaction constants λ nm corresponding to the strong electron-phonon coupling renormalized in the two band case and to the presence of Coulomb interaction µ * nm [86,87]. 2.…”

Microscopic theory of superconductivity in MgB2-type systems in a magnetic field: A neighborhood of H c2

“…This condition is satisfied for the compound MgB 2 , in which the σ band is more responsible for superconductivity. In [14], we obtained renormalized constants λ nm (see (12)) of the electron-phonon interaction for MgB 2 using the theory of the thermodynamic properties of two-band superconductors and the condition that the values of T c , ∆ 1 , and ∆ 2 and also the heat capacity jump at the point T = T c correspond to the experimental data obtained for the compound MgB 2 . We obtained the following numerical values: λ 11 = 0.302, λ 22 = 0.135, λ 12 = 0.04, and λ 21 = 0.06.…”

“…Using the two-band model [6], we can obtain high T c , two energy gaps ∆ 1 and ∆ 2 (the conditions 2∆ 1 /T c > 3.5 and 2∆ 2 /T c < 3.5 are satisfied), small values of the jump of the electron specific heat at the point T = T c (this jump is equal to 0.8 for MgB 2 and to 1.43 in the one-band case), the anomalous temperature dependence of the specific heat in the superconducting phase, the positive curvature of the upper critical field H c2 , and other characteristics [11]. We note that the theory of two-band superconductivity for systems with a variable density of charge carriers [12], [13], when applied to MgB 2 [14], leads to a good agreement of the thermodynamic characteristics with the experimental data in the case where other elements of the periodic table substitute for the Mg and B atoms.…”