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

Abstract

We calculate the upper critical magnetic field Hc2 in the framework of a microscopic superconductivity theory with two energy bands of different dimensions on the Fermi surface with the cavity topology typical of the compound MgB2 taken into account (an anisotropic system). We assume an external magnetic field parallel to the crystallographic z axis. We obtain analytic formulas in the low-temperature range (T /Tc 1) and also near the critical temperature`(T − Tc)/Tc 1´. We compare the temperature dependence of Hc2 for a two-band anisotropic system with that of H 0 c2 corresponding to a two-band isotropic system (with Fermi-surface cavities of the same topology). We determine the role of the bandstructure anisotropy, the positive curvature of the upper critical field near the critical temperature, and the important role of the ratio v1/v2 of the velocities on the Fermi surface in determining Hc2. We also obtain the values of the parameters ∆1 and ∆2 along the line of the critical magnetic field.

The Upper Critical Field H c2 in Advanced Superconductors with Anisotropic Energy Spectrum

“…(3.21) and relation (3.25) defining the chemical potential as well as Eq. (4.21) for upper critical field (for detail, see [34]). We shall use the electron-phonon interaction constant corresponding to MgB 2 (see Sect.…”

“…In this work, the results are presented briefly and concisely, they allow understanding the overall picture of occurring processes. For more details of this problem, in addition to [9], see [27] and [33][34][35][36].…”

Analytical solutions of the microscopic two-band theory for the temperature dependence of the upper critical fields of pure MgB2 compared with experimental data

“…If we use the values of λ nm , v 1 , v 2 and other theory parameters from [19] and [20] in order to compare this theoretical approach with experiments on MgB 2 , we will obtain a qualitative agreement between them [32][33][34][35][36]; this can be explained, in particular, by inexact determination of the theory parameters (the spread of these values in the literature is quite substantial). In this work we transform the expressions for H c2 (ab) and H c2 (c) in the studied temperature range introducing coefficients at all temperature dependent terms (see, e.g., (21)).…”

“…2.2, we can the analytical solutions of Eq. (33) by substituting in (34) the asymptotic values of the functions in the following range of values (a) T c -T << T c , ρ n << 1 and (b) T << T c , ρ n >> 1 and keeping the terms with the core contribution, see [33,36]. These solutions can be represented as follows: a) At temperatures near the critical (T c -T << T c ) we obtain the following formula for the temperature dependence of the upper critical field: …”

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

“…Thus, we apply the technique of Maki and Tsuzuki, extended for the two-band case [92] with the accounting of MgB 2 compound band structure peculiarities (for details see [94][95][96]). 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.…”