Superconductivity through Hubbard Model
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Date
2007-07
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Addis Ababa University
Abstract
Superconductivity through Hubbard model has been studied following Hartree Fock
Approximation. The theoretical study has been made on the origin of superconductivity
in electron-electron interaction with coulomb repulsion which is not phononic.
The former interaction is under some condition, qualitatively different as compared
to the latter interaction . The study by considering a Hubbard model is focused and
brought out by applying the canonical transformation method as well as by simple
renormalization operation that excludes double occupancy in the effective Hubbard
Hamiltonian of the system and goes over in to the t-J model Hamiltonian that serves
as a reference point (fixed point ). For small deviations from half filling holes move in
the antiferromagnetic lattice and create disorder and establishes superconductivity.
This Hamiltonian is used and theoretically examined in the second quantization notation
by using Green’s function formalism and suitable decoupling approximations
the survival of superconductivity has been shown with the computation of supper
conducting order parameter ( ) and transition temperature (Tc) mathematically to
make known its possibility. The phase diagram of the numerical estimates of the
superconducting transition temperature versus values of electron (hole) boson coupling
constant has been obtained and it is in agreement with the the experimental
observation. We found that supper conductivity is obtained through Hubbard model
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Keywords
Hubbard Model