Efeitos das interações elétron-elétron na supercondutividade convencional

Abstract

Seeking to contribute to the understanding of the superconductivity phenomenon, we investigate the effects that electron-electron interactions can have on the superconducting phase. We describe the BCS theory of John Bardeen, Leon Cooper, and John Robert Schrieffer, which is used to describe conventional superconductors where superconductivity occurs due to electron-electron coupling caused by phonon sin the lattice of the superconducting material. However, materials that are not described by this theory have attracted much interest since the 1980s, not only because they challenge a well-established theory but also because they exhibit important characteristics, such as the conducting phase at high temperatures. We propose an approach where we construct a model by adding a Fermi liquid-type interaction term to the BCS Hamiltonian. With this, we obtain the self-consistent equations for this model and write a computer program capable of solving them. As a result, we obtain graphs that represent the effects of the Fermi liquid term on the superconducting order parameters. We then point out that this term affects the Fermi surface of the system, potentially deforming it, and that this added term is capable of inducing superconducting phases with different symmetries coexisting.