THE STUDY OF COMPETITION BETWEEN SUPERCONDUCTIVITY AND SPINDENSITYWAVE IN ELECTRON DOPED LANTHANUM IRON ARSENIC OIXDE SUPERCONDUCTOR (LaFeAsO1-XFX)

Abstract In this work we study based on the competition between superconductivity and spin density wave in electron doped LaFeAsO1-xFx. The competition between superconductivity and spin density wave had attracted immense interest and effort following the discovery of cup rate and the recent iron based superconductors. The magnetic order is the result of nesting between holes pocket found at the center of Brillion zone and electron pockets found at the corner of the Brillion zone .The interaction between electrons and holes forming these pockets is very important to study the low energy physics. The formulation of the model Hamiltonian consisting of holes and electrons responsible for magnetic and superconducting pairing interactions and Using a model of the Hamiltonian and retarded double time green function formalism, we found mathematical the expression for superconducting transition temperature (TC), superconducting order parameter (sc), AFM order parameter (), and AFM transition temperature (Tm) and we study the coexistence between AFM spin density wave and superconducting state. From the correlation of superconducting transition temperature with superconducting order parameters and magnetic transition temperature with magnetic order parameter , it is observed that when the temperature increases superconducting order parameter decrease and vanish at temperature equal to the critical temperature (TC) whereas magnetic transition temperature (Tm) is directly proportional to the magnetic order parameter .we obtained the phase diagrams (TC Vs ) and (Tm Vs ) to obtained the region where both orders i.e magnetism and superconductivity coexist. The region under the intersection of the two merged graphs shows that the AFM and superconductivity in electron doped of the system is finely intertwined (LaFeAsO1-XFX)