Superconductivity is the disappearance of DC electrical resistance in a material when it is cooled to a certain critical temperature, when a material changes from normal state to superconducting state when it is cooled to a certain critical temperature is known as phase transition. Superconductivity occur when electronphonon interaction is attractive and this occur when the energy difference between the electronic states involved is less than the phonon energy, and vice versa, that the critical temperature for transition to the superconducting state depends on the isotopic mass. This pointed to the possibility that the superconducting transition involved some kind of interaction with the crystal lattice. This electron-phonon interaction is likely to overcome the Coulomb repulsion and binds the fermions into pairs which then condense and super conduct. In exotic pairing three electrons take part in the superconducting current and that they interact with each other through harmonic forces. Two of these electrons form a bound pair while the third one is a polarization electron which hops from one lattice site to another lattice site of similar symmetry. The polarization electron causes perturbations leading to contraction of p 3 Cu O bond. Three types of possible interactions between electrons in the crystal that are believed to cause transition to superconducting phase are explored theoretically using perturbation theory. According to the theory of second quantization, if a perturbation commutes with the rest of the Hamiltonian, it leads to a phase transition. The objective of the study is to investigate the commutability of the three interactions if it can lead to phase transition of a superconductor: The three types of interactions are interaction of electrons through phonons exchange, simultaneous existence of electron-phonon interaction and Coulomb interaction, and exotic pairing of electrons. Thus the interactions commute and can lead to a phase transition, and they can be used to study the properties of superconductors.

University of Eldoret



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