Electronic Structure of Cuprates in a Boson–Fermion Mixture Theory

Abstract

In a nearly‐filled energy band where scattering of electrons is hampered, a pairing interaction between two electrons and quanta in a solid (e.g., phonons or spin‐resonances or some other excitation of electronic origin) can still occur in the s‐channel where a field quantum mediates the coalescence of two fermions into a new composite particle. By describing the attractively‐interacting electrons as a gas mixture of individual electrons plus bosons made up of two electrons, the dependence on momentum of the energy of single electrons is investigated. When the net interaction BCS dimensionless coupling constant λ and the ratio with the maximum energy of a quantum mediating the pairing to the Fermi energy increases, the coalescence of electrons at temperatures higher than the Bose–Einstein condensation (BEC) temperature of bosons leads to the appearance of steep (waterfall‐like) changes in the high‐energy electron spectrum of the binary boson–fermion (BF) gas mixture. These waterfall‐like anomalies seen in high‐ superconductors (HTSCs) are in fact a characteristic property of a BF gas mixture and reflect the splitting of the conduction band into two subbands emerging as the number of two‐electron bosons increases.