Study of ARPES data and d-wave superconductivity using electronic models in two dimensions

We review the results of an extensive investigation of photoemission spectral weight using electronic models for the high-Tc superconductors. Here we show that some recently reported unusual features of the cuprates namely the presence of (i) flat bands, (ii) small quasiparticle bandwidths, and (iii) antiferromagnetically induced weight, have all a natural explanation within the context of holes moving in the presence of robust antiferromagnetic correlations. Introducing interactions among the hole carriers, a model is constructed which has ${\rm d_{x^2 - y^2}}$ superconductivity, an optimal doping of $\sim 15\%$ (caused by the presence of a large density of states at the top of the valence band), and a critical temperature $\sim 100K$.Comment: 11 pages Z-compressed postscript, to appear in the Proceedings to the Stanford Conference on Spectroscopies in Novel superconductor

On Some Complex Aspects of the (2+1)-dimensional Broer-Kaup-Kupershmidt System

The improved Bernoulli sub-equation function method is used in extracting some new exponential function solutions to the (2+1)-dimensional Broer-Kaup-Kupershmidt system. It is of vital effort to look for more solutions of the (2+1)-dimensional Broer-Kaup-Kupershmidt system, which are very helpful for coastal and civil engineers to apply the nonlinear water models in a harbor and coastal design. All the obtained solutions satisfied the (2+1)-dimensional Broer-Kaup-Kupershmidt system. The two- and three-dimensional shapes of all the obtained solutions in this paper are also presented. All the computations and the graphics plots in this study are carried out with the aid of the Wolfram Mathematica 9

The Spin Gap in the Context of the Boson-Fermion Model for High TcT_c Superconductivity

The issue of the spin gap in the magnetic susceptibility $\chi''(q,\omega)$ in high T_c superconductors is discussed within a scenario of a mixture of localized tightly bound electron pairs in singlet states (bi-polarons) and itinerant electrons. Due to a local exchange between the two species of charge carriers, antiferromagnetic correlations are induced amongst the itinerant electrons in the vicinity of the sites containing the bound electron pairs. As the temperature is lowered these exchange processes become spatially correlated leading to a spin wave-like spectrum in the subsystem of the itinerant electrons. The onset of such coherence is accompanied by the opening of a pseudo gap in the density of states of the electron subsystem whose temperature dependence is reflected in that of $\chi'' (q,\omega)$ near $q =(\pi,\pi)$ where a ``spin gap'' is observed by inelastic neutron scattering and NMR.Comment: 9 pages Latex, 3 figures available upon request. To appear in Physica

Disorder and Impurities in Hubbard-Antiferromagnets

We study the influence of disorder and randomly distributed impurities on the properties of correlated antiferromagnets. To this end the Hubbard model with (i) random potentials, (ii) random hopping elements, and (iii) randomly distributed values of interaction is treated using quantum Monte Carlo and dynamical mean-field theory. In cases (i) and (iii) weak disorder can lead to an enhancement of antiferromagnetic (AF) order: in case (i) by a disorder-induced delocalization, in case (iii) by binding of free carriers at the impurities. For strong disorder or large impurity concentration antiferromagnetism is eventually destroyed. Random hopping leaves the local moment stable but AF order is suppressed by local singlet formation. Random potentials induce impurity states within the charge gap until it eventually closes. Impurities with weak interaction values shift the Hubbard gap to a density off half-filling. In both cases an antiferromagnetic phase without charge gap is observed.Comment: 16 pages, 9 figures, latex using vieweg.sty (enclosed); typos corrected, references updated; to appear in "Advances in Solid State Physics", Vol. 3

Asymmetry of the electron spectrum in hole-doped and electron-doped cuprates

Within the t-t'-J model, the asymmetry of the electron spectrum and quasiparticle dispersion in hole-doped and electron-doped cuprates is discussed. It is shown that the quasiparticle dispersions of both hole-doped and electron-doped cuprates exhibit the flat band around the (\pi,0) point below the Fermi energy. The lowest energy states are located at the (\pi/2,\pi/2) point for the hole doping, while they appear at the (\pi,0) point in the electron-doped case due to the electron-hole asymmetry. Our results also show that the unusual behavior of the electron spectrum and quasiparticle dispersion is intriguingly related to the strong coupling between the electron quasiparticles and collective magnetic excitations.Comment: 8 pages, 3 figures, typo corrected, added detailed calculations and updated figure 3 and references, accepted for publication in Phys. Lett.

Hole Doping Evolution of the Quasiparticle Band in Models of Strongly Correlated Electrons for the High-T_c Cuprates

Quantum Monte Carlo (QMC) and Maximum Entropy (ME) techniques are used to study the spectral function $A({\bf p},\omega)$ of the one band Hubbard model in strong coupling including a next-nearest-neighbor electronic hopping with amplitude $t'/t= -0.35$. These values of parameters are chosen to improve the comparison of the Hubbard model with angle-resolved photoemission (ARPES) data for $Sr_2 Cu O_2 Cl_2$. A narrow quasiparticle (q.p.) band is observed in the QMC analysis at the temperature of the simulation $T=t/3$, both at and away from half-filling. Such a narrow band produces a large accumulation of weight in the density of states at the top of the valence band. As the electronic density $$ decreases further away from half-filling, the chemical potential travels through this energy window with a large number of states, and by $\sim 0.70$ it has crossed it entirely. The region near momentum $(0,\pi)$ and $(\pi,0)$ in the spectral function is more sensitive to doping than momenta along the diagonal from $(0,0)$ to $(\pi,\pi)$. The evolution with hole density of the quasiparticle dispersion contains some of the features observed in recent ARPES data in the underdoped regime. For sufficiently large hole densities the ``flat'' bands at $(\pi,0)$ cross the Fermi energy, a prediction that could be tested with ARPES techniques applied to overdoped cuprates. The population of the q.p. band introduces a {\it hidden} density in the system which produces interesting consequences when the quasiparticles are assumed to interact through antiferromagnetic fluctuations and studied with the BCS gap equation formalism. In particular, a region of extended s-wave is found to compete with d-wave in the overdoped regime, i.e. when the chemical potential has almost entirely crossed the q.p.Comment: 14 pages, Revtex, with 13 embedded ps figures, submitted to Phys. Rev. B., minor modifications in the text and in figures 1b, 2b, 3b, 4b, and 6

The Superconducting Instabilities of the non half-filled Hubbard Model in Two Dimensions

The problem of weakly correlated electrons on a square lattice is formulated in terms of one-loop renormalization group. Starting from the action for the entire Brillouin zone (and not with a low-energy effective action) we reduce successively the cutoff $\Lambda$ about the Fermi surface and follow the renormalization of the coupling $U$ as a function of three energy-momenta. We calculate the intrinsic scale $T_{co}$ where the renormalization group flow crosses over from the regime ($\Lambda > T_{co}$) where the electron-electron (e-e) and electron-hole (e-h) terms are equally important to the regime ($\Lambda < T_{co}$) where only the e-e term plays a role. In the low energy regime only the pairing interaction $V$ is marginally relevant, containing contributions from all renormalization group steps of the regime $\Lambda > T_{co}$. After diagonalization of $V_{\Lambda =T_{co}}$, we identify its most attractive eigenvalue $\lambda _{\min}$. At low filling, $\lambda _{\min}$ corresponds to the $B_2$ representation ($d_{xy}$ symmetry), while near half filling the strongest attraction occurs in the $B_1$ representation ($d_{x^2-y^2}$ symmetry). In the direction of the van Hove singularities, the order parameter shows peaks with increasing strength as one approaches half filling. Using the form of pairing and the structure of the renormalization group equations in the low energy regime, we give our interpretation of ARPES experiments trying to determine the symmetry of the order parameter in the Bi2212 high-$T_{c}$ compound.Comment: 24 pages (RevTeX) + 11 figures (the tex file appeared incomplete

d-Wave Model for Microwave Response of High-Tc Superconductors

We develop a simple theory of the electromagnetic response of a d- wave superconductor in the presence of potential scatterers of arbitrary s-wave scattering strength and inelastic scattering by antiferromagnetic spin fluctuations. In the clean London limit, the conductivity of such a system may be expressed in "Drude" form, in terms of a frequency-averaged relaxation time. We compare predictions of the theory with recent data on YBCO and BSSCO crystals and on YBCO films. While fits to penetration depth measurements are promising, the low temperature behavior of the measured microwave conductivity appears to be in disagreement with our results. We discuss implications for d-wave pairing scenarios in the cuprate superconductors.Comment: 33 pages, plain TeX including all macros. 16 uuencoded, compressed postscript figures are appended at the en