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

Magnetic flux can penetrate a type-II superconductor in the form of Abrikosov vortices (also called flux lines, flux tubes, or fluxons) each carrying a quantum of magnetic flux phi 0=h/2e. These tiny vortices of supercurrent tend to arrange themselves in a triangular flux-line lattice (FLL), which is more or less perturbed by material inhomogeneities that pin the flux lines, and in high-Tc superconductors (HTSCs) also by thermal fluctuations. Many properties of the FLL are well described by the phenomenological Ginzburg-Landau theory or by the electromagnetic London theory, which treats the vortex core as a singularity. In Nb alloys and HTSCs the FLL is very soft mainly because of the large magnetic penetration depth lambda . The shear modulus of the FLL is c66~1/ lambda 2, and the tilt modulus c44(k)~(1+k2 lambda 2)-1 is dispersive and becomes very small for short distortion wavelengths 2 pi /k<< lambda . This softness is enhanced further by the pronounced anisotropy and layered structure of HTSCs, which strongly increases the penetration depth for currents along the c axis of these (nearly uniaxial) crystals and may even cause a decoupling of two-dimensional vortex lattices in the Cu-O layers. Thermal fluctuations and softening may `melt` the FLL and cause thermally activated depinning of the flux lines or ofthe two-dimensional `pancake vortices` in the layers. Various phase transitions are predicted for the FLL in layered HTSCs. Although large pinning forces and high critical currents have been achieved, the small depinning energy so far prevents the application of HTSCs as conductors at high temperatures except in cases when the applied current and the surrounding magnetic field are small.

https://iopscience.iop.org/article/10.1088/0034-4885/58/11/003/pdf

The flux-line lattice in superconductors

Magnetic flux can penetrate a type-II superconductor in form of Abrikosov vortices. These tend to arrange in a triangular flux-line lattice (FLL) which is more or less perturbed by material inhomogeneities that pin the flux lines, and in high-$T_c$ supercon- ductors (HTSC's) also by thermal fluctuations. Many properties of the FLL are well described by the phenomenological Ginzburg-Landau theory or by the electromagnetic London theory, which treats the vortex core as a singularity. In Nb alloys and HTSC's the FLL is very soft mainly because of the large magnetic penetration depth: The shear modulus of the FLL is thus small and the tilt modulus is dispersive and becomes very small for short distortion wavelength. This softness of the FLL is enhanced further by the pronounced anisotropy and layered structure of HTSC's, which strongly increases the penetration depth for currents along the c-axis of these uniaxial crystals and may even cause a decoupling of two-dimensional vortex lattices in the Cu-O layers. Thermal fluctuations and softening may melt the FLL and cause thermally activated depinning of the flux lines or of the 2D pancake vortices in the layers. Various phase transitions are predicted for the FLL in layered HTSC's. The linear and nonlinear magnetic response of HTSC's gives rise to interesting effects which strongly depend on the geometry of the experiment.

The Flux-Line Lattice in Superconductors

We have previously shown that Tc for Bi2 (Sr, Ca)n+1CunO2n+4+δ (n=1, 2 and 3) varies with oxygen stoichiometry δ determined by annealing in a variety of oxygen partial pressures and temperatures. Annealing results are now also presented for several Tl-superconductors in the series Tlm(Ba, Sr)2Can−1CunO2n+m+2+δ, for both m=1 and 2, revealing two general results for this class of Bi or TI superconductors: (1) effects on Tc due to labile oxygen occur for all m=2 compounds but are absent in m = 1 compounds with Sr. m=1 compounds with Ba do have variable oxygen but the effects on the c-axis are the opposite to m=2 compounds. This suggests for the latter that the labile oxygen resides in interstitial sites within the Bi2O2 or Tl2O2 bi layers; (2) the hole concentration per Cu decreases in progressing from n = 1 to 2 to 3 in either class so that the parent n = 3 and n = 2 compounds lie respectively on the low- and high-hole concentration sides of the peak in Tc while the n = 1 compounds extend out into the non-superconducting domain at very high hole concentration.

/pdf/general-trends-in-oxygen-stoichiometry-effects-on-tc-in-bi-4gmly6ibdk.pdf

General trends in oxygen stoichiometry effects on Tc in Bi and Tl superconductors

A new superconductor that displays onset behavior near 120 K has been identified as Bi2Sr3-xCaxCu2O8+y, with x ranging from about 0.4 to 0.9. Single crystal x-ray diffraction data were used to determine a pseudo-tetragonal structure based on an A-centered orthorhombic subcell with a = 5.399 A, b= 5.414A, and c = 30.904 A. The structure contains copper-oxygen sheets as in La2CuO4 and YBa2Cu3O7, but the copper-oxygen chains present in YBa2Cu3O7 do not occur in Bi2Sr3-xCaxCu2O8+y. The structure is made up of alternating double copper-oxygen sheets and double bismuth-oxygen sheets. There are Ca2+ and Sr2+ cations between the adjacent Cu-O sheets; Sr2+ cations are also found between the Cu-O and Bi-O sheets. Electron microscopy studies show an incommensurate superstructure along the a axis that can be approximated by an increase of a factor of 5 over the subcell dimension. This superstructure is also observed by x-ray diffraction on single crystals, but twinning can make it appear that the superstructure is along both a and b axes. Flux exclusion begins in our samples at about 116 K and is very strong by 95 K. Electrical measurements on a single crystal of Bi2Sr3-xCaxCu2O8+y show a resistivity drop at about 116 K and apparent zero resistivity at 91 K.

https://science.sciencemag.org/content/sci/239/4843/1015.full.pdf

A New High-Temperature Superconductor: Bi2Sr3-x Cax Cu2O8+y.

A series of oxygen-defect perovskites containing CuII and CuIII: The oxides La3−xLnxBa3 [CuII5−2y CuIII1+2y] O14+y

A new superconductor Pb 0.5 Sr 2.5 Y 0.5 Ca 0.5 Cu 2 O 7−δ has been isolated whose superconducting properties depend upon the thermal treatments, i.e. are closely related to the oxygen stoichiometry. This material exhibits a T on c =100 K whereas the T off c ( R =0) ranges from 45 K to 53 K. The magnetic measurements using a SQUID magnetometer show superconducting volume fractions ranging from 14% to 72%. Anomalies appear in the magnetization curves at low field for some samples. This effect and the broad transition are interpreted in terms of an inhomogeneous distribution of oxygen in the matrix. The structure of this tetragonal phase ( a =3.81 A, c =11.908 A) belongs to the “1212” type observed for thallium cuprates, i.e. consists of an intergrowth of double rock salt-type layers involving lead and strontium and of double copper pyramidal layers interleaved with yttrium and calcium. This oxide differs also from the classical intergrowth structures by the existence of numerous oxygen vacancies in the rock salt type layers (δ≅0.7−0.5); moreoer satellites are observed on E.D. diffraction patterns. These two effects are explained by the presence of the 6s 2 lone pair of Pb(II).

Superconductivity up to 100 K in lead cuprates: A new superconductor Pb0.5Sr2.5Y0.5Ca0.5Cu2O7−δ

Lattice imaging (HREM) of the defects induced by 5.3 GeV Pb ions in YBa 2 Cu 3 O 7−δ ( δ ⩽ 0.1) ceramics provides evidence of latent tracks formation whose influence on the electron transport properties ( R , J c ) has been studied. It is clearly established that the electronic energy loss plays a predominant role in the radiation damage mechanism of 1-2-3 superconductors whenever the energy deposited by inelastic collisions exceeds a threshold value close to 8 MeV μm . A track induced enhancement of the critical magnetization current density is observed at low fluences ( φt ⩽ 3 × 10 11 cm −2 ) but it appears to depend on the value and the orientation of the applied magnetic field with respect to the direction of the tracks.

Latent track formation induced by high energy heavy ions in superconductive copper oxides

The effects of 35-GeV Xe ion irradiation on the superconducting (T/sub c/, J/sub c/) and normal (R) properties of the high-T/sub c/ superconductors YBa/sub 2//sub Z/Cu/sub 3/O/sub 7-//sub delta/ with 01less than or equal todelta<07 have been investigated by means of n situ resistance measurements between 42 and 105 K It is shown that the decrease of the T/sub c/ offset and the concomitant increase of the resistance in the normal state are strongly enhanced by inelastic collisions which lead to the production of discontinuous tracks of extended defects visualized by high-resolution electron microscopy These defects act as pinning centers for the flux lines and result in the improvement of the critical density J/sub c/ by a factor of 35 (H = 0, T = 5 K) for a Xe fluence of 25 x 10/sup 11/ cm/sup -2/ The greater sensitivity to irradiation damage of the phases corresponding to low oxygen contents (delta = 046 and 062) has been attributed to the particular structure of these compounds which exhibit, as has been previously reported, intergrowths of insulating YBa/sub 2/Cu/sub 3/O/sub 6/ regions or chains with superconducting YBa/sub 2/C/sub 3/O/sub 7/ regions or chains

Modifications of the physical properties of the high-Tc superconductors YBa2Cu3O7- delta (0.1 <= delta <0.7) by 3.5-GeV xenon ion bombardment.

During the investigation of the system Bi—Sr—Cu—O a novel family of superconducting oxides, close to the composition Sr2Bi2Cu207+δhas been isolated, with a midpoint critical temperature ranging from 7 K to 22 K. The X-ray diffraction and high-resolution electron microscopy studies have shown its relationships with perovskite and demonstrated its bidimensional character. The possible relationships of this lamellar oxide with Aurivillius phases is discussed.

J. Provost

Papers

A series of oxygen-defect perovskites containing CuII and CuIII: The oxides La3−xLnxBa3 [CuII5−2y CuIII1+2y] O14+y

Superconductivity up to 100 K in lead cuprates: A new superconductor Pb0.5Sr2.5Y0.5Ca0.5Cu2O7−δ

Latent track formation induced by high energy heavy ions in superconductive copper oxides

Modifications of the physical properties of the high-Tc superconductors YBa2Cu3O7- delta (0.1 <= delta <0.7) by 3.5-GeV xenon ion bombardment.

Superconductivity in the Bi — Sr — Cu — O System