Since the discovery of superconductivity above 30 K by Bednorz and M\"uller in the La copper oxide system, the critical temperature has been raised to 90 K in Y${\mathrm{Ba}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ and to 110 and 125 K in Bi-based and Tl-based copper oxides, respectively. In the two years since this Nobel-prize-winning discovery, a large number of electronic structure calculations have been carried out as a first step in understanding the electronic properties of these materials. In this paper these calculations (mostly of the density-functional type) are gathered and reviewed, and their results are compared with the relevant experimental data. The picture that emerges is one in which the important electronic states are dominated by the copper $d$ and oxygen $p$ orbitals, with strong hybridization between them. Photon, electron, and positron spectroscopies provide important information about the electronic states, and comparison with electronic structure calculations indicates that, while many features can be interpreted in terms of existing calculations, self-energy corrections ("correlations") are important for a more detailed understanding. The antiferromagnetism that occurs in some regions of the phase diagram poses a particularly challenging problem for any detailed theory. The study of structural stability, lattice dynamics, and electron-phonon coupling in the copper oxides is also discussed. Finally, a brief review is given of the attempts so far to identify interaction constants appropriate for a model Hamiltonian treatment of many-body interactions in these materials.

Electronic structure of the high-temperature oxide superconductors

We report local-density-functional calculations of hybridization matrix elements and effective electron-electron interactions in ${\mathrm{La}}_{2}$Cu${\mathrm{O}}_{4}$ defining a general effective Hamiltonian that we propose as an appropriate starting point for many-body calculations in this material. The parameter values lend support to an Anderson lattice model. We find the impurity approximation to this model yields a magnetic ground state of ${x}^{2}\ensuremath{-}{y}^{2}$ symmetry, a 1-2-eV insulating gap bounded by ionization and affinity levels of the same symmetry, and a calculated $d$ spectral weight in qualitative agreement with photoemission experiments. We discuss anticipated modification of these results by lattice effects.

Calculated effective Hamiltonian for La2CuO4 and solution in the impurity Anderson approximation.

Electronic structure and properties of YBa2Cu3O7-δ, a low dimensional, low density of states superconductor

https://repository.library.northeastern.edu/files/neu:331186/fulltext.pdf

A survey of the Van Hove scenario for high-tc superconductivity with special emphasis on pseudogaps and striped phases

Measurements of the transport critical‐current density (Jc), magnetization Jc, and magnetoresistance in a number of bulk sintered samples of Y1Ba2Cu3Ox from several different laboratories indicate that the transport Jc is limited by weak‐link regions between high Jc regions. The weak‐link Jc has a Josephson character, decreasing by two orders of magnitude as the magnetic field is increased from 0.1 to 10 mT at 77 K. An examination of the grain‐boundary region in Y1Ba2Cu3Ox shows no observable impurities or second phases to the scale of the [001] lattice planes (∼12 A). The effect of intrinsic conduction anisotropy is discussed. A current‐transfer model is proposed in which weak conduction along the c axis plays a role in limiting Jc at grain boundaries. Orienting the grains in the powder state during processing may result in enhanced transport Jc in bulk conductors.

D.D. Koeling

Papers

Bonds, bands, charge transfer excitations and superconductivity of YBa2Cu3O7-δ