The Electronic Structure of High T c Copper-Oxide Superconductors from Photoemission Spectroscopy
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sélect emitted électrons of a particular value of crystal momentum k. The basic conceptual issues concerning the electronic structure revolve around the fact that the normal metallic state of the superconductors is achieved by doping "parent" insulating antiferromagnetic (AFM) Cu-O materials which belong to a class of transition métal oxides which are insulators, not because of a gap in the underlying band structure, as with an ordinary semiconductor, but because of Coulomb repulsion between the transition métal 3d électrons 13 . This situation is commonly modeled by the one-band Hubbard Hamiltonian3 in which there is a single électron orbital on each lattice site, électrons hop by a one-electron matrix élément fq between orbitals on sites i and j , and there is a Coulomb repulsion U between two électrons on the same site. In HTSC materials, attention is focused on the electronic structure of planes of Cu and O atoms. The Cu is regarded as a Cu2+d9 ion and the single d-hole per Cu site is modeled4 by a half-filled Hubbard band. If LZ=0, one obtains the band structure by diagonalizing the tij with Bloch waves, and if the band is half filled, the ground state is a métal. The métal has some fraction of unoccupied and doubly occupied sites, which are energetically
unfavorable if U is large. For U » tp the ground state is an insulator with one électron localized on each site.1"3. The PES/IPES spectrum 3 has filled and empty parts are separated by a "corrélation gap" U. The Anderson superexchange theory2 shows that the residual effect of fij induces AFM ordering of the localized électron spins. What sort of electronic structure is produced by adding holes or électrons to such an insulator, and does the BCS theory apply to the superconducting state? In considering thèse questions, we recall that there exist some basic ideas, known collectively as Fermi liquid theory (FLT), which provide a firm rationale for the band picture of the near-EF states of real metals with interacting électrons. An important part of this picture is a counting theorem, due to Luttinger,5 which states that the volume enclosed by the Fermi surface is preserved as Coulomb interactions are turned on, so long as the ground state symmetry is unchanged. Thus, for example, in an isotropic system the Fermi momentum kF is preserved. Obviously, the split spectrum of the correlated insulator at half-filling lies outside thèse ideas. With this background, we mention three possible doping scénarios: 1. If the PES/IPES spectrum of the insulator is assumed to be rigid, then the Fermi level for hole or électron doping would lie in the lower or upper part of the correlation-split spectrum, respectively. The states near the Fermi energy would retain much of the character of the correlated insulator. 2. Perhaps, when the HTSC parent insulator is doped to the metallic state, the Luttinger theorem and other Fermi liquid ideas once again apply; i.e., band theory has direct relevance to the nearEF states of the métal.6 3. An élégant scénario4 with aspects of both (1) and
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