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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Date
2017-11-05
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Addis Ababa University
Abstract
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.
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Keywords
Study on the Interplay, Local and Itinerant, Electrons In Iron Based, Superconducting Materials, Coulomb Interaction