Investigation of superconducting properties in two-band model for the iron based high temperature superconductor $$Ba_{1-x}K_{x}Fe_{2}As_{2}$$ B a 1 - x K x F e 2 A s 2

The current research work deals with the theoretical study of the superconducting order parameters, superconducting transition temperature, density of states and condensation energy in two-band model for the iron-based superconductor Ba $$_{1-x}$$ 1 - x K $$_{x}$$ x Fe $$_{2}$$ 2 As $$_{2}$$ 2 . In this study we considered the electron and hole intra band interactions and the inter-band interaction between the two bands in the Bardeen, Cooper and Schrieffer (BCS) mean field approximation (MFA) level for Ba $$_{1-x}$$ 1 - x K $$_{x}$$ x Fe $$_{2}$$ 2 As $$_{2}$$ 2 . By formulating a system Hamiltonian in two-band model and by employing the Green’s function technique and equation of motion method, we obtained the mathematical expressions for the temperature dependence of superconducting order parameters in the electron intra-band interaction, $$\Delta _{e}(T)$$ Δ e ( T ) ; hole intra-band interaction, $$\Delta _{h}(T)$$ Δ h ( T ) ; inter-band interaction, $$\Delta _{eh}(T)$$ Δ eh ( T ) and in the combined intra-inter band interactions, $$\Delta _{intra-inter}(T)$$ Δ i n t r a - i n t e r ( T ) for Ba $$_{1-x}$$ 1 - x K $$_{x}$$ x Fe $$_{2}$$ 2 As $$_{2}$$ 2 . By using the experimental values and by considering some plausible approximations of the parameters in the obtained expressions, phase diagrams of superconducting order parameters, $$\Delta _{e}$$ Δ e , $$\Delta _{h}$$ Δ h , $$\Delta _{eh}$$ Δ eh and $$\Delta _{intra-inter}$$ Δ i n t r a - i n t e r versus temperature are plotted. We also obtained the mathematical expression for the dependence of the superconducting transition temperature $$(T_{C})$$ ( T C ) on the inter-band interaction potential $$(V_{eh}$$ ( V eh ) and a phase diagram is plotted for the material under consideration. Moreover, we obtained the mathematical expressions for the dependence of density of states on excitation energy and temperature in the electron and hole intra-band interactions and phase diagrams are plotted for Ba $$_{1-x}$$ 1 - x K $$_{x}$$ x Fe $$_{2}$$ 2 As $$_{2}$$ 2 . Furthermore, we have investigated the dependence of condensation energy $$(E_{c})$$ ( E c ) on temperature and on inter-band interaction potential and phase diagrams are plotted based on the obtained mathematical expressions for Ba $$_{1-x}$$ 1 - x K $$_{x}$$ x Fe $$_{2}$$ 2 As $$_{2}$$ 2 . The results we obtained in this research work for the theoretical enhancement of the superconducting order parameter up to, $$\Delta _{intra-inter}(0)\simeq 20$$ Δ i n t r a - i n t e r ( 0 ) ≃ 20 meV and the superconducting transition temperature up to, $$T_{C}\approx 61$$ T C ≈ 61 K for the Fe-based superconductor Ba $$_{1-x}$$ 1 - x K $$_{x}$$ x Fe $$_{2}$$ 2 As $$_{2}$$ 2 are the main reasons for the novelty of this research work. The results we obtained in this work are in broad agreement with previous experimental findings. Graphical abstract