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

Abstract

A brief review of works on the microscopic theory of determining the upper critical field in twoband isotropic and anisotropic superconductors is given. The research is based on a set of the Ginzburg-Landau equations for the order parameters in a magnetic field that are studied in terms of the classical approach to a superconducting system in a magnetic field. Two inequivalent energy bands with different topology of Fermi surface cavities overlapping on the Fermi surface are discussed. The cases of the direction of the external magnetic field // the (ab) plane and // the crystallographic c axis are studied. The equations for determining H c2 (ab) and H c2 (c) for a pure superconductor and a superconductor doped with electrons and holes are derived. The analytical solutions to these equations in the vicinity of the superconducting transition temperature (T c -T<<T c ) and in the vicinity of zero (T<<T c ) are found. The temperature and impurity dependences of the upper critical fields H c2 (ab) and H c2 (c), as well as the anisotropy coefficient H , are studied. The resulting theory is applied to determine the dependences of the above magnetic characteristics of intermetallic compound MgB 2 . The theory agrees qualitatively with experimental data.

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

“…22 , Refs. 32-35, and review article [36]. It follows from these works that the temperature dependences of H c2 (ab) and H c2 (c) are consistent with theoretical results [23][24][25][26] and available experimental data.…”

“…Note that technique [29] contains two main parts: the execution, if possible, of all operations on the right-hand side of Eq. (4) (for details see [36], Appendix A) and the execution of a number of mathematical transformations in terms of the microscopic theory of superconductivity [34][35][36]. In this way, set of Eq.…”

“…For each of these cases we obtain asymptotic expressions for functions fnm. We shall substitute the values of these functions into (16) with some preliminary simplifications (for details see [34] and Appendix B in [36]). Thereupon, we obtain: …”

“…Therefore, it is unnecessary to introduce a parameter controlling the deviation of the σ-band from the 2D behavior making the problem less anisotropic (for details see [36]). …”

“…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: …”