Theoretical models for high-temperature superconductivity

Summary A semi-phenomenological analysis is given of the effects of certain band structure features on the gap ratios 2Δ/k _B T _c for high-T _c superconductors, including multigap systems. In addition to phonons other intermediate bosons (IB) mediating the superconducting interaction are considered. Interesting results emerge when the IB energy exceeds the widths of possible narrow peaks in the density of states associated with subbands presumably belonging to substructures such as stacked Cu−O planes. Comparison with experiment is made. In particular, data obtained by Warrenet al. via nuclear-spin relaxation on Ba₂YCu₃O_7−δ can be interpreted within the present framework in terms of a model having an IB of energy ≳1 eV, which exceeds the predicted width (≲0.3 eV) of a peak in the density of states containing the normal-state Fermi level. This suggests that the IB is not a phonon. To speed up publication, the author of this paper has agreed to not receive the proofs for correction.     

Antiferromagnetism and high-temperature superconductivity

A model is presented describing superconductivity in close association with antiferromagnetism in a narrow-band system with electron correlations. We employ the Hubbard-Peierls Hamiltonian for weak to intermediate ratios between the on-site Coulomb repulsion and the electronic band width. Depending on the band structure and the electron number density antiferromagnetism arises, which for a nearly half-filled band gives rise to a Mott-Hubbard gap and resultant band splitting. The related density of energy states exhibits a singularity at the upper and lower edge of the lower and upper of the two split bands, respectively, if the lattice possesses the property of perfect nesting. The electron-phonon interaction is recast, by help of the method of canonical transformations, into a new form implying an attractive interaction between the quasiparticles in a Debye shell near the Fermi surface of each subband. A large effective interaction constant can be achieved and a BCS-type model for superconduction applies to each of the split bands if they are partially filled. Pairing arises between quasiparticles with parallel effective spin, i.e. in triplet states. The resulting gap equation is discussed in detail and the thermodynamic potential of the superconducting antiferromagnet is derived.     

New picture of high-temperature superconductivity

The case for high-temperature superconductivity originating in SrO or BaO planes, or in interstitial regions, is made, including (i) four successfully predicted superconductors; (ii) evidence that the superconductivity of the major cuprates is associated with holes in these layers; (iii) data showing that Pr on one side of a cuprate-plane kills the superconductivity, but Pr on the other side does not; and (iv) evidence that doped Sr₂YRuO₆ has an onset of superconductivity at ∼45 K despite having no cuprate-planes.     

Multiphase percolation and Josephson model for high-temperature superconductivity

A four-phase percolation problem is used to simulate the Josephson model for high-temperature superconductivity both as a four-phase and a three-phase system. We implement the method on an IBM PC microcomputer using PASCAL language.     

Theory of high-temperature superconductivity in cuprates

A microscopic theory of electronic spectrum and superconducting pairing in the high-temperature cuprate superconductors is presented. The theory is based on consideration of strong electron correlations within the Bogolyubov polar model. The Dyson equation is derived by using the equation of motion method for the thermodynamic Green functions in terms of the Hubbard operators. The self-energy is evaluated in the noncrossing approximation for electron scattering on spin and charge fluctuations induced by kinematic interaction. The theory demonstrates that a strong Coulomb repulsion results in the anomalous electronic spectrum and unconventional (d-wave) superconducting pairing with high T _c mediated by the antiferromagnetic exchange and spin fluctuations.     

Possible superconductivity mechanism in high-temperature superconductors

The formation temperature (T*~ 135 K) is determined in the Shubin-Vonsovski approximation for local electron pairs in the CuO₂ planes of YBa₂Cu₃O₇ crystal. This estimate is used to obtain the Coulomb pseudopotential µ*≈?0.15. In the presence of strong electron-phonon coupling (λ ~0.5) and electron correlation in the electron pairing, the estimate of critical temperature T _c ≈99 K agrees, by the order of magnitude, with its experimental value. The calculated ratio 2Δ/kT _c ≈4.13 confirms the presence of strong electron pairing.     

Kinematic spin-fluctuation mechanism of high-temperature superconductivity

We study d-wave superconductivity in the extended Hubbard model in the strong correlation limit for a large intersite Coulomb repulsion V. We argue that in the Mott-Hubbard regime with two Hubbard subbands, there emerges a new energy scale for the spin-fluctuation coupling of electrons of the order of the electron kinetic energy W much larger than the exchange energy J. This coupling is induced by the kinematic interaction for the Hubbard operators, which results in the kinematic spin-fluctuation pairing mechanism for V ? W. The theory is based on the Mori projection technique in the equation of motion method for the Green’s functions in terms of the Hubbard operators. The doping dependence of the superconductivity temperature T _c is calculated for various values of U and V.     

Chiral Nonlinear sigma models as models for topological superconductivity

We study the mechanism of topological superconductivity in a hierarchical chain of chiral nonlinear sigma models (models of current algebra) in one, two, and three spatial dimensions. The models illustrate how the 1D Fr?hlich's ideal conductivity extends to a genuine superconductivity in dimensions higher than one. The mechanism is based on the fact that a pointlike topological soliton carries an electric charge. We discuss a flux quantization mechanism and show that it is essentially a generalization of the persistent current phenomenon, known in quantum wires. We also discuss why the superconducting state is stable in the presence of a weak disorder.     

Toward a topological scenario for high-temperature superconductivity of copper oxides

The structure of the joint phase diagram demonstrating high-$T_c$ superconductivity of copper oxides is studied on the basis of the theory of interaction-induced flat bands. Prerequisites for an associated topological rearrangement of the Landau state are established, and related non-Fermi-liquid (NFL) behavior of the normal states of cuprates is investigated. We focus on manifestations of this behavior in the electrical resistivity $\rho (T)$, especially the observed gradual crossover from normal-state T-linear behavior $\rho (T,x)=A_1(x)T$ at doping x below the critical value $x_c^h$ of hole doping for termination of superconductivity, to T-quadratic behavior at $x>x_c^h$, which is incompatible with predictions of the conventional quantum-critical-point scenario. It is demonstrated that the slope of the coefficient $A_1$ is universal, being the same on both boundaries of the joint phase diagram of cuprates, in agreement with available experimental data.     

Electronic plus phonon-exchange mechanism for high-temperature superconductivity in layered crystals

A general mathematical formulation is developed for calculating the effective electron-electron interaction in layered crystals like YBa₂Cu₃O_7−δ, and for finding the resulting superconducting transition temperatureT _c in such systems within the framework of the conventional BCS pairing arising from various possible excitations in the medium. This differs considerably from the usual case of an effective three-dimensional homogeneous system, and should be relevant in the calculation ofT _c for the new class of high-T _c perovskites in which oxygen deficiencies in Cu-O layers and their distribution in the crystal play a crucial role. The explicit form of the effective interactionV _jj(q _t,ω) in a given layerj in the unit cell of the crystal is found to be determined not only by the true polarization functionπ _j(q _t,ω) of that layer, but also of other layers. The exchange of electronic excitations of a nearby insulating layer by carriers in a conducting layer thus becomes possible to get highT _c, with or without the usual phonon exchange.