Superconductivity through Hubbard Model

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Addis Ababa University


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



Hubbard Model