Regular Article

Theoretical investigation of the coexistence of superconductivity and spin density wave (SDW) in two-band model for the iron-based superconductor BaFe₂(As_1−xP_x)₂

¹ Department of Physics, Adigrat University, Adigrat, Ethiopia
² Department of Physics, College of Science, Bahir Dar University, Bahir Dar, Ethiopia
³ Department of Physics, Mekelle University, Mekelle, Ethiopia

^a e-mail: tsadik.k@gmail.com

Received: 11 November 2017
Received in final form: 29 October 2018
Published online: 18 February 2019

Abstract

This study focuses on the theoretical investigation of the coexistence of superconductivity and spin density wave (SDW) in a two-band model for the iron-based superconductor BaFe₂(As_1−xP_x)₂. By employing a system Hamiltonian in a two-band model for a given system and by using the double time temperature dependent Green’s function formalism at the Bardeen-Cooper-Schrieffer (BCS) mean field approximation (MFA) level, we obtained mathematical expressions for the dependence of superconducting transition temperature (T_C) on SDW order parameter (Δ_SDW) in the electron and hole intra-band interactions, and in the inter-band interactions for superconductor BaFe₂(As_1−xP_x)₂. Similarly, we have obtained an expression for the dependence of SDW transition temperature (T_SDW) on the SDW order parameter (Δ_SDW) for BaFe₂(As_1−xP_x)₂. By using experimental values and considering some plausible approximations of the parameters in the obtained expressions, phase diagrams of T_C versus Δ_SDW in the electron and hole intra-band interactions, and in the inter-band interactions are plotted for the BaFe₂(As_1−xP_x)₂ superconductor. Similarly, a phase diagram of T_SDW versus Δ_SDW is plotted for the same superconductor. By merging the two phase diagrams, we have demonstrated the possible coexistence of superconductivity and SDW in the electron and hole intra-band interactions, and in the inter-band interactions for BaFe₂(As_1−xP_x)₂. Furthermore, we have investigated the dependence of Δ_SDW on temperature in pure SDW region and the phase diagram is plotted for the variation of Δ_SDW with temperature for superconductor BaFe₂(As_1−xP_x)₂. Our findings are in agreement with previous experimental results.