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

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.

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

Disorder-enhanced delocalization and local-moment quenching in a disordered antiferromagnet

The interplay of disorder and spin-fluctuation effects in a disordered antiferromagnet is studied. In the weak-disorder regime (W \le U), while the energy gap decreases rapidly with disorder, the sublattice magnetization, including quantum corrections, is found to remain essentially unchanged in the strong correlation limit. Magnon energies and Neel temperature are enhanced by disorder in this limit. A single paradigm of disorder-enhanced delocalization qualitatively accounts for all these weak disorder effects. Vertex corrections and magnon damping, which appear only at order (W/U)^4, are also studied. With increasing disorder a crossover is found at W \sim U, characterized by a rapid decrease in sublattice magnetization due to quenching of local moments, and formation of spin vacancies. The latter suggests a spin-dilution behavior, which is indeed observed in softened magnon modes, lowering of Neel temperature, and enhanced transverse spin fluctuations.Comment: 12 pages, includes 8 postscript figures. To appear in Physical Review B. References adde

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

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

Magnetic correlations and quantum criticality in the insulating antiferromagnetic, insulating spin liquid, renormalized Fermi liquid, and metallic antiferromagnetic phases of the Mott system V_2O_3

Magnetic correlations in all four phases of pure and doped vanadium sesquioxide V_2O_3 have been examined by magnetic thermal neutron scattering. While the antiferromagnetic insulator can be accounted for by a Heisenberg localized spin model, the long range order in the antiferromagnetic metal is an incommensurate spin-density-wave, resulting from a Fermi surface nesting instability. Spin dynamics in the strongly correlated metal are dominated by spin fluctuations in the Stoner electron-hole continuum. Furthermore, our results in metallic V_2O_3 represent an unprecedentedly complete characterization of the spin fluctuations near a metallic quantum critical point, and provide quantitative support for the SCR theory for itinerant antiferromagnets in the small moment limit. Dynamic magnetic correlations for energy smaller than k_BT in the paramagnetic insulator carry substantial magnetic spectral weight. However, the correlation length extends only to the nearest neighbor distance. The phase transition to the antiferromagnetic insulator introduces a sudden switching of magnetic correlations to a different spatial periodicity which indicates a sudden change in the underlying spin Hamiltonian. To describe this phase transition and also the unusual short range order in the paramagnetic state, it seems necessary to take into account the orbital degrees of freedom associated with the degenerate d-orbitals at the Fermi level in V_2O_3.Comment: Postscript file, 24 pages, 26 figures, 2 tables, accepted by Phys. Rev.

Superconducting Order Parameter Symmetry in Multi-layer Cuprates

We discuss the allowed order parameter symmetries in multi-layer cuprates and their physical consequences using highly non-specific forms of the inter- and intra-plane interactions. Within this framework, the bi-layer case is discussed in detail with particular attention paid to the role of small orthorhombic distortions as would derive from the chains in YBCO or superlattice effects in BSCCO. In the orthorhombic bi-layer case the (s,-s) state is of special interest, since for a wide range of parameters this state exhibits pi phase shifts in corner Josephson junction experiments. In addition, its transition temperature is found to be insensitive to non-magnetic inter-plane disorder, as would be present at the rare earth site in YBCO, for example. Of particular interest, also, are the role of van Hove singularities which are seen to stabilize states with d_{x^2 - y^2}-like symmetry, (as well as nodeless s-states) and to elongate the gap functions along the four van Hove points, thereby leading to a substantial region of gaplessness. We find that d_{x^2 - y^2}-like states are general solutions for repulsive interactions; they possess the fewest number of nodes and therefore the highest transition temperatures. In this way, they should not be specifically associated with a spin fluctuation driven pairing mechanism.Comment: REVTeX documentstyle, 34 pages, 10 figures include