Theoretical Investigation of the Interplay of Superconductivity and Magnetism in Ba1-xKxFe2As2 Superconductor in a Two-Band Model by Using the Bogoliubov Transformation Formalism

The main focus of this article is to investigate the theoretical interplay of magnetism and superconductivity in a two-band model for the iron-based superconductor Ba1-xKxFe2As2. On the basis of experimental results, the two-band model Hamiltonian was considered. We obtained mathematical statements for the superconductor Ba1-xKxFe2As2 superconducting (SC) transition temperature, spin-density-wave (SDW), transition temperature, superconductivity order parameter, and SDW order parameter from the Bogoliubov transformation formalism and the model Hamiltonian. Furthermore, an expression for the dependence of the SDW transition temperature on the SDW order parameter and the dependence of the SC transition temperature on the SDW order parameter was obtained for Ba1-xKxFe2As2. By substituting the experimental and theoretical values of the parameters in the derived statements, phase diagrams of the SC transition temperature versus the SDW order parameter and the SDW transition temperature versus the SDW order parameters have been plotted to demonstrate the dependence of the SDW order parameter on transition temperatures. By combining the two-phase diagrams, we depicted the possible coexistence of superconductivity and magnetism for the Ba1-xKxFe2As2 superconductor. The phase diagrams of temperature versus SC order parameter and temperature versus SDW order parameter were also plotted to show the dependence of order parameters on temperature for the Ba1-xKxFe2As2 superconductor.