Extended Saddle Point Singularities Research Articles

Abrikosov and the path to understanding high-Tc superconductivity

An early attempt to try to understand the high superconducting transition temperatures in the cuprate super-conductors was Abrikosov's theory of extended Van Hove singularities. It was based on our early experimental data on the YBa2Cu3O6.9 and YBa2Cu4O8 compounds which showed an extended saddle point singularity in the dispersion of the electronic excitations. This appeared to lead to a Van Hove singularity in the density of states with a divergence stronger than the known logarithmic one observed in conventional materials. The consequent high density of states of the extended singularity was thought to lead to high Tc's in a conventional BCS mechanism. Unfortunately, it was soon realized that the very incoherent nature of the electronic excitations in these materials did not provide the expected high density of states. Here we summarize the many unusual characteristics of the electronic excitations in the cuprates, and what they imply for a possible theoretical description of high-temperature superconductivity.

Properties of the pseudogap phase in high-Tcsuperconductors

Several physical properties of the pseudogap phase are calculated on the basis of the spatially inhomogenous Franz-Millis model of superconducting fluctuations, consisting of small superconducting domains with uncorrelated supercurrents. The variation of this domain structure with time is supposed to be slow. A distribution function of superfluid velocities is found based on the assumption of the dominant role of extended saddle point singularities (``hot spots''). The model is used for calculation of the spectral function, the inelastic neutron scattering cross section, and the spin susceptibility entering the Knight shift. In all cases the calculated curves are qualitatively close to experimental results.

Fine structure of the neutron maximum in high-temperature superconducting cuprates

A calculation is performed of the imaginary part of the electron magnetic susceptibility, as function of energy and momentum in the vicinity of the maximum of the inelastic neutron scattering. Compared to the previous calculation a slight bending of the energy bands in the vicinity of extended saddle point singularities is taken into account. It is shown that this simple picture fits qualitatively the recently observed experimental data on the fine structure in momentum space of the inelastic neutron scattering cross section in the vicinity of the maximum at different energies.

Theory of high-Tc superconducting cuprates based on experimental evidence

A model of superconductivity in layered high-temperature superconducting cuprates is proposed, based on the extended saddle point singularities in the electron spectrum, weak screening of the Coulomb interaction and phonon-mediated interaction between electrons plus a small short -range repulsion of Huid's, or spin-fluctuation origin. This permits to explain the large values of Tc, features of the isotope effect on oxygen and copper, the existence of two types of the order parameter, the peak in the inelastic neutron scattering, the positive curvature of the upper critical field, as function of temperature etc.

THEORY OF HIGH-Tc SUPERCONDUCTING CUPRATES BASED ON EXPERIMENTAL EVIDENCE

A model of superconductivity in layered high-temperature superconducting cuprates is proposed, based on the extended saddle point singularities in the electron spectrum, weak screening of the Coulomb interaction and phonon-mediated interaction between electrons plus a small short-range repulsion of Hund's, or spin-fluctuation, origin. This permits to explain the large values of T c , features of the isotope effect on oxygen and copper, the existence of two types of the order parameter, the peak in the inelastic neutron scattering, the positive curvature of the upper critical field, as function of temperature etc.

About the Influence of the Square-Root Van Hove Singularity on the Critical Temperature of Overdoped High-Temperature Superconductors

It is shown that the square-root van Hove singularity in the density of states ν(E F )~ (E F -E0)-1/2, associated with the extended saddle-point singularities in the electron spectra of the cuprates, leads to a nonmonotonic dependence of the critical temperature T c on the position of the Fermi level E F with respect to the bottom E0 of the saddle. As a result of cancellation of the divergency of ν(E F ) in the electron–electron coupling constant, renormalized due to the account of the strong coupling effects, T c approaches zero in the limit E F → E0. This result contrasts that of the weak coupling approximation, which gives a finite value of T c for E F → E0. The T c on the concentration of doped holes, obtained in the strong coupling approximation, agrees qualitatively with the experimental data for the overdoped cuprate metal-oxides.

Electronic structure of planar superconducting systems.: From finite to extended model

A 4-site 4-electron model is extended to a square planar CuO 2 sheet. The degeneracy at the Fermi level can be split in different ways and this results in a charge density wave ground state, with alternating charges on the metal sites, or an anti-ferromagnetic ground state with spin correlation. If these two states are nearly equal in energy, a magnetic ground state may appear in a perpendicular magnetic field, with persistent currents in the ground state and with paired spins. The tight-binding model is used for square planar systems with L loops and (2 L) 2 sites. The 2 L-fold degenerate eigenvalue x=0, consistent with the Van Hove singularity, has exact eigenvector solutions which can be used as generators for other possible solutions. In the magnetic state persistent currents exist in the ground state of the hole-doped infinite system. A novel explanation is given for the `extended saddle point singularity' of the energy bands below T c. Some other properties of type II superconductors may also be explained, such as the d-wave symmetry of the pair wave function.

Current transport through low-angle grain boundaries in high-temperature superconductors

We consider mechanisms which can account for the observed rapid decrease of the critical current density ${J}_{c}(\ensuremath{\theta})$ with the misorientation angle $\ensuremath{\theta}$ through grain boundaries (GB's) in high-${T}_{c}$ superconductors (HTS's). We show that the ${J}_{c}(\ensuremath{\theta})$ dependence is mostly determined by the decrease of the current-carrying cross section by insulating dislocation cores and by progressive local suppression of the superconducting order parameter $\ensuremath{\psi}$ near GB's as $\ensuremath{\theta}$ increases. The insulating regions near the dislocation cores result from a strain-induced local transition to the insulating antiferromagnetic phase of HTS's. The structure of the nonsuperconducting core regions and current channels in GB's is strongly affected by the anisotropy of the strain dependence of ${T}_{c}$ which is essentially different for ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7}$ and Bi-based HTS's. We propose a mechanism of the progressive superconductivity suppression on GB's with $\ensuremath{\theta}$ due to an excess ion charge on the GB's which shifts the chemical potential in the layer of the order of screening length ${l}_{D}$ near the GB's. The local suppression of $\ensuremath{\psi}$ is amplified by the proximity of all HTS's to a metal-insulator transition, by their low carrier density and extended saddle point singularities in the electron density of states near the Fermi surface. Taking into account these mechanisms, we calculated ${J}_{c}(\ensuremath{\theta})$ analytically by solving the Ginzburg-Landau equation. The model well describes the observed quasiexponential decrease of ${J}_{c}(\ensuremath{\theta})$ with $\ensuremath{\theta}$ for many HTS's. The $d$-wave symmetry of the order parameter weakly affects ${J}_{c}(\ensuremath{\theta})$ in the region of small $\ensuremath{\theta}$ and cannot account for the observed drop of ${J}_{c}(\ensuremath{\theta})$ by several orders of magnitude as $\ensuremath{\theta}$ increases from 0 to $\ensuremath{\theta}\ensuremath{\simeq}20\ifmmode^\circ\else\textdegree\fi{}--40\ifmmode^\circ\else\textdegree\fi{}$.

About the hall effect temperature anomalies in the normal state of high-T c superconductors

The temperature anomalies of the Hall effect in the normal state of high-T c superconductors are explained in the framework of two-band model and conventional electron - phonon scattering mechanisms. The essential feathers of the proposed model are: 1) strong hybridization of the narrow band with the broad one near the Fermi level, which results in highly anisotropic two-branch spectrum; 2) striking difference in the values of transport and cyclotron masses of nondegenerated carriers at the upper branch and degenerated holes at the lower one due to the extended saddle point singularity; 3) nonzero probability of interbranch scattering.

Isotope-shift exponent and the gap ratio within the extended saddle point singularity scenario for different pairing symmetries

Exact analytical expressions for the isotope-shift exponent are derived within the BCS formalism for different pairing symmetries (isotropic s-wave, extended s-wave, d-wave) and extended saddle point singularity in the density of states (DOS) is considered. The isotope-shift exponent and the gap ratio are studied as a function of doping for different symmetries. It is found that the predictions for the d-wave pairing symmetry are closer to the experimental situation in cuprates.

Superconductivity in the Strong Coupling Limit: Van Hove Singularity and Extended Saddle Point Singularity Scenario

The effect of orthorhombic distortion and second nearest neighbor hopping on the transition temperature (T c ) and the isotope-shift exponent (α) have been studied for a two dimensional system, within the framework of Eliashberg formalism in the van Hove singularity scenario. The behavior of T c and α have been discussed for the case of extended saddle point singularity. A comparison of the strong coupling theory results is made with the results of weak coupling theory. From our study it reveals that the effect of singularity in the density of states (DOS) in the strong coupling limit is not so significant as that in weak coupling case.

One-hole motion in the two-dimensional frustrated t-J model.

The influence of a frustration term in the exchange part of the t-J model onto the dispersion relation of one hole has been investigated. We have chosen two independent methods, namely, a variational ansatz which describes a magnetic polaron of minimal size and the exact diagonalization method of a 4\ifmmode\times\else\texttimes\fi{}4 lattice. It has been found that the frustration shifts the minimum from the point (\ensuremath{\pi}/2,\ensuremath{\pi}/2) to the point (0,\ensuremath{\pi}) in k space. It has also been shown that the frustration term alone does not lead to the correct, experimentally observed flat dispersion region around (0,\ensuremath{\pi}). A better agreement with the observed, extended saddle point singularity may be obtained by simulating the decrease of spin correlations due to a finite temperature. \textcopyright{} 1996 The American Physical Society.

On the nature of the order parameter in htsc and influence of impurities

A model of superconductivity in layered high-temperature superconducting cuprates is proposed, based on the extended saddle point singularities in the electron spectrum, weak screening of the Coulomb interaction and phonon-mediated interaction between electrons plus a small short-range repulsion of Hund's or spin-fluctuation origin. This permits to explain the large values of T c , features of the isotope effect, photoemission results for the gap and the seemingly conflicting results of Josephson experiments in various geometries. The influence of impurity scattering on T c , the order parameter at T = 0 and the density of states, including the energy gap, are studied for the same model. It is shown that the suppression of the gap in the vicinities of the singularities is weak, and the same is true for T c . Since the order parameter beyond the singularity is still defined by its value in the singular region, it scales with this value and varies only slightly. However, the energy gap in this region, which does not coincide with the order parameter, varies rapidly with impurity concentration, and the gap becomes isotropic in the strong scattering limit. These conclusions agree with preliminary experimental observations.

Parity of the order parameter in high-temperature superconductors with respect to a pi /2 rotation.

In order to establish the parity of the order parameter in the model based on the idea of a strong phonon-mediated long-range attraction, enhanced by the extended saddle-point singularities in the electron spectrum, plus a weak short-range repulsion, a comparison of critical temperatures and free energies of the even and odd solutions for the order parameter is performed. A criterion is established distinguishing the two options. It is shown, particularly, that superconductivity, induced by phonons, can, nevertheless, lead to an odd order parameter. On the other hand, contrary to the previous statements, this is the only possibility for the order parameter to change its sign within this model. The theory is influenced by the latest experimental results.

On the nature of the order parameter in HTSC and influence of impurities

The previously proposed model, based on the extended saddle point singularities in the electron spectrum, weak screening of the Coulomb interaction and phonon-mediated interaction between electrons, is supplemented by a small short-range repulsion of Hund's or spin-fluctuation origin. This permits one to explain the change of sign of the order parameter in a natural way and to resolve the seeming conflicts between existing experimental data. The influence of impurity scattering on T c, the order parameter at T = 0 and the density of states, including the energy gap, are studied for the same model. A simple argument shows that the small-angle scattering due to ionized impurities does not change the superconducting parameters, and all changes come from the large-angle scattering. For the vicinity of the singularity the “out scattering” has a small probability, since the density of states beyond the singularity is low. Therefore, the suppression of the gap in this vicinity is weak, and the same is true for T c. On the other hand, the scattering of electrons distant from the singularity into the singular region is much larger, due to the enhanced density of states. Since the order parameter beyond the singularity is still defined by its value in the singular region, it scales with this value and varies only slightly. However, the energy gap in this region, which does not coincide with the order parameter, increases rapidly with impurity concentration so that the gap becomes isotropic in the strong scattering limit. These conclusions agree with preliminary experimental observations.

Observation of a van Hove singularity in Bi2Sr2CaCu2O8+x with angle-resolved photoemission.

We have performed high energy resolution angle-resolved photoemission studies of the normal state band structure of oxygen overdoped $Bi_{2}Sr_{2}Ca_{1}Cu_{2}O_{8+x}$. We find that there is an extended saddle point singularity in the density of states along $\Gamma-\bar{M}-Z$ direction. The data also indicate that there is an asymmetry in the Fermi surface for both the $\Gamma-\bar{M}-Z$ and perpendicular directions.

Experimentally observed extended saddle point singularity in the energy spectrum of YBa 2Cu 3O 6.9 and YBa 2Cu 4O 8 and some of the consequences

Angle-resolved photoemission experiments show that the high temperature superconductors YBa 2Cu 3O 6.9 and YBa 2Cu 4O 8 have a spectral density which exhibits an “extended” saddle point singularity along the Γ-Y symmetry direction, centered on the Y point. This, in turn, leads to a van Hove singularity in the density of states with a divergence stronger than the well-known logarithmic one. We examine the consequences of this singularity in several limiting cases on the superconducting transition temperature, the ratio 2Δ(0)/ T c, and the isotope effect. We conclude that this singularity alone, although it can possibly lead to sufficiently high transition temperatures and a vanishingly small isotope effect, does not explain the ratio of 2Δ(0)/ T c∼6 observed experimentally.