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

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Addis Ababa University


In this dissertation the interplay of localized and itinerant electrons in iron based superconducting systems using the Hubbard model is theoretically studied. By developing a model Hamiltonian for the system and by using quantum field theory Green’s function formalism, we have obtained mathematical expressions for superconducting transition temperature(TC), spin density wave transition temperature(Tsdw), superconductivity order parameter(_Sc) and spin density wave order parameter(_sdw). By employing the experimental and theoretical values of the parameters in the obtained expressions, phase diagrams of superconducting transition temperature(TC) versus superconducting order parameter(_Sc) and spin density wave transition temperature (Tsdw) versus spin density wave order parameter(_sdw) have been plotted. By combining the two phase diagrams, the possible coexistence of superconductivity and spin density wave (SDW) in Ferropnictide Ba1−xKxFe2As2 is demonstrated. Thus, in both the SDW and SC phases, the coexistence of the itinerant electrons and the local moments are crucial to the underlying mechanisms. Starting with a model Hamiltonian consisting of a pairing interaction, magnetic interactions of Heisenberg type by local electrons and an interaction of itinerant electrons with localized electrons and using Greens function technique, the expressions for superconducting order parameter (_(T)) and the superconducting transition temperature, TC are determined. The expressions indicate that magnetization suppresses superconductivity, and there might be a coexistence below critical temperature. The result also suggest the importance of the concept of localized and itinerant electron system in theoretical work. Moreover, the exchange field dependence of the Hubbard model with a attractive, effective, xi xii pairwise, nearest neighbour interaction via the Hartree-Fock-Gorkov approximation is explore. Based on the spin-generalised Bogoliubov-de-Gennes (BdG) equations, we obtained expressions of gap equations (superconducting order parameters), specific heat capacity, Magnetization and magnetic susceptibility for singlet and triplet superconductors in the presence and absence of exchange field is obtained. By developing the model Hamiltonian for the system and using the double time temperaturedependent Greens function formalism, the expressions for superconducting transition temperature (Tc) as a function of electron coupling constant (_elc), equation of motion for parallel and anti parallel spin pairing and temperature dependent of magnetization for both itinerant and localized electrons hoping with intra and inter Coulomb interactions is obtained. Based on the general features of multi-bands and intermediate coupling strengths, a phenomenological theory of coexistence of itinerant and localized electrons have been proposed to describe the low-energy physics in iron-based superconductors. By using the experimental and theoretical values of the parameters in the obtained expressions, the plots of superconducting transition temperature versus electron coupling constant (_elc), superconducting transition temperature (Tc ) versus superconducting order parameter (_) and magnetization vesus superconducting transition temperature are plotted and demonstrated the possibility of the interplay of itinerant and localized electrons in iron based superconductors.



Study on the Interplay, Local and Itinerant, Electrons In Iron Based, Superconducting Materials, Coulomb Interaction