The Study On The Interplay Of Local And Itinerant Electrons In Iron Based Superconducting Materials Using Hubbard Model Hopping With Intra And Inter Coulomb Interaction

In this dissertation the interplay of localized and itinerant electrons in iron basedrnsuperconducting systems using the Hubbard model is theoretically studied. By developingrna model Hamiltonian for the system and by using quantum field theory Green’srnfunction formalism, we have obtained mathematical expressions for superconductingrntransition temperature(TC), spin density wave transition temperature(Tsdw), superconductivityrnorder parameter(_Sc) and spin density wave order parameter(_sdw). Byrnemploying the experimental and theoretical values of the parameters in the obtainedrnexpressions, phase diagrams of superconducting transition temperature(TC) versusrnsuperconducting order parameter(_Sc) and spin density wave transition temperaturern(Tsdw) versus spin density wave order parameter(_sdw) have been plotted. By combiningrnthe two phase diagrams, the possible coexistence of superconductivity and spinrndensity wave (SDW) in Ferropnictide Ba1−xKxFe2As2 is demonstrated. Thus, inrnboth the SDW and SC phases, the coexistence of the itinerant electrons and the localrnmoments are crucial to the underlying mechanisms. Starting with a model Hamiltonianrnconsisting of a pairing interaction, magnetic interactions of Heisenberg type byrnlocal electrons and an interaction of itinerant electrons with localized electrons andrnusing Greens function technique, the expressions for superconducting order parameterrn(_(T)) and the superconducting transition temperature, TC are determined. The expressionsrnindicate that magnetization suppresses superconductivity, and there mightrnbe a coexistence below critical temperature. The result also suggest the importancernof the concept of localized and itinerant electron system in theoretical work. Moreover,rnthe exchange field dependence of the Hubbard model with a attractive, effective,rnxirnxiirnpairwise, nearest neighbour interaction via the Hartree-Fock-Gorkov approximationrnis explore. Based on the spin-generalised Bogoliubov-de-Gennes (BdG) equations,rnwe obtained expressions of gap equations (superconducting order parameters), specificrnheat capacity, Magnetization and magnetic susceptibility for singlet and tripletrnsuperconductors in the presence and absence of exchange field is obtained. By developingrnthe model Hamiltonian for the system and using the double time temperaturedependentrnGreens function formalism, the expressions for superconducting transitionrntemperature (Tc) as a function of electron coupling constant (_elc), equation of motionrnfor parallel and anti parallel spin pairing and temperature dependent of magnetizationrnfor both itinerant and localized electrons hoping with intra and inter Coulomb interactionsrnis obtained. Based on the general features of multi-bands and intermediaterncoupling strengths, a phenomenological theory of coexistence of itinerant and localizedrnelectrons have been proposed to describe the low-energy physics in iron-basedrnsuperconductors. By using the experimental and theoretical values of the parametersrnin the obtained expressions, the plots of superconducting transition temperaturernversus electron coupling constant (_elc), superconducting transition temperature (Tcrn) versus superconducting order parameter (_) and magnetization vesus superconductingrntransition temperature are plotted and demonstrated the possibility of therninterplay of itinerant and localized electrons in iron based superconductors.

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