Effect of doping on spin density wave & superconductivity in electron-doped iron Pnictide superconductors

We formulate a Hamiltonian model to investigate the effects of doping on superconductivity and spin density wave in electron-doped iron pnictide superconductors. The model, which is based on the BCS mechanism, employs a mean-field approach. The equations of motion for single-particle electron Green’s functions are derived from Zubarev type electron Green’s function. Single-particle correlation functions were derived by analysing the quasi-particle energies. The superconducting (SC) gap (z), spin density wave (SDW) gap (h) and chemical potential ($\mu$) were determined self-consistently and numerically for various dopant concentrations (x). The results indicate that as doping levels increase, the SDW gradually weakens, leading to the onset of superconductivity. In the doping range $x=0.045-0.06$, a coexistence of the SDW and superconductivity is observed. Further doping results in the suppression of the spin density wave, accompanied by a rise in the superconducting critical temperature, which reach 26 K at $x=0.07$. The phase diagram depicting the relationship between the SDW Neel Temperature, SC critical temperature and doping parameter agrees well with experimental observations.