Theoretical investigation of the coexistence of superconductivity and spin density wave (SDW) in two-band model for the iron-based superconductor BaFe2(As1-xPx)2

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(As1-xPx)(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 ((SDW)) in the electron and hole intra-band interactions, and in the inter-band interactions for superconductor BaFe2(As1-xPx)(2). Similarly, we have obtained an expression for the dependence of SDW transition temperature (T-SDW) on the SDW order parameter((SDW))for BaFe2(As1-xPx)(2). By using experimental values and considering some plausible approximations of the parameters in the obtained expressions, phase diagrams of T-C versus (SDW) in the electron and hole intra-band interactions, and in the inter-band interactions are plotted for theBaFe(2)(As1-xPx)(2) superconductor. Similarly, a phase diagram of T-SDW versus (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(As1-xPx)(2). Furthermore, we have investigated the dependence of (SDW) on temperature in pure SDW region and the phase diagram is plotted for the variation of (SDW) with temperature for superconductor BaFe2(As1-xPx)(2). Our findings are in agreement with previous experimental results.