On the Quasi-Particle Spectra of YBA₂CU₃O₇

Abstract

As is well known, the phenomenon of superconductivity arises when in a metal electrons pair up and occupy a single quantum state. Since electrons normally repel each other, one of the principal questions in the case of any superconductor is ”why do such Cooper pairs form?”. Whilst for the conventional superconductors the answer is that the attraction is due to the electron-phonon coupling, in the case of the new, high temperature, superconductors (HTSC)¹, in spite of the unprecedented effort of the past few years, the physical cause of the pairing remains a mystery². Rather than speculating on the microscopic nature of the pairing, in this paper, we implement a semi-phenomenological strategy, whose aim is to determine which local orbitals the electrons occupy when they experience the attraction. Of course, because our description of pairing is semi-phenomenological, we shed new light on the physical mechanism of pairing only indirectly. As will be shown presently, progress towards such a goal is made possible, in principle, by a particularly efficient representation of the electron-electron interaction afforded by the Density Functional Theory (DFT) of Superconductivity^3,4 and, in practice, by the development of powerful numerical methods for solving the corresponding Kohn-Sham-Bogoliubov-de Gennes (KS-BdG) equation^5,6. A central feature of this theory is an electron-electron interaction kernel K(r ₁,r′₁;r ₂,r′₂) which, when corresponding to an attractive interaction, leads to superconductivity. This attractive interaction is parametrized by a set of interaction constants K _{RL, R′L′} , where R, R′ and L, L′ refer to the positions and orbital character, respectively, of the two electrons.