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arXiv:cond-mat/9704193 · Physical review. B, Condensed matter

Friedel oscillations induced by nonmagnetic impurities in the two-dimensional Hubbard model

W. Ziegler, H. Endres, Werner R. Hanke

Published Aug 15, 1998• 9 citations
arXivHTMLPDF

Abstract

We study the interplay of correlations and disorder using an unrestricted slave-Boson technique in real space. Within the saddle-point approximation, we find Friedel oscillations of the charge density in the vicinity of a single nonmagnetic impurity, in agreement with numerical simulations. The corresponding amplitudes are suppressed by repulsive interactions, while attractive correlations lead to a charge-density-wave enhancement. In addition, we investigate the spatial dependence of the local magnetic moment and the formation of a magnetic state at the impurity site.

DOI
10.1103/physrevb.58.4362

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We study the interplay of correlations and disorder using an unrestricted slave-Boson technique in real space. Within the saddle-point approximation, we find Friedel oscillations of the charge density in the vicinity of a single nonmagnetic impurity, in agreement with numerical simulations. The corresponding amplitudes are suppressed by repulsive interactions, while attractive correlations lead to a charge-density-wave enhancement. In addition, we investigate the spatial dependence of the local magnetic moment and the formation of a magnetic state at the impurity site.
Using numerical techniques we study the zero-temperature properties of a substitutional magnetic impurity in a one-dimensional correlated system described by the Hubbard model with repulsive interaction U. We find that, while the static spin correlation maintains a 2kF{\mathit{k}}_{\mathit{F}}kF​ periodicity, the charge correlations show Friedel oscillations with a 4kF{\mathit{k}}_{\mathit{F}}kF​ periodicity for large values of U. The static on-site susceptibility decreases as the interactions in the chain are turned on and we interpret this as an increase of the Kondo temperature. For large values of U the short-range antiferromagnetic correlations dominate over the collective Kondo singlet formation.
We study interference patterns and Friedel oscillations (FO) due to scattering from two or more localized impurities and scattering from extended inhomogeneities in the two-dimensional lattice systems of interacting fermions. Correlations between particles are accounted for by using an approximate method based on the real-space dynamical mean-field theory and a homogeneous self-energy approximation (HSEA), where the site-dependent part of the self-energy is neglected. We find that the interference maxima and minima change systematically as we vary the relative distance between the two impurities. At the same time, the increase of the interaction does not shift the position of interference fringes but only reduces their intensities. A comparison with the single impurity cases clearly shows complex patterns in FO fringes induced by additional multiple scattering processes. In the case of an extended steplike potential the system becomes more homogeneous when the interaction increases. FO and interference patterns are not present in the Mott insulating phase in both single and many impurity models.
Magnetic correlations are studied in a two-leg Hubbard ladder doped with nonmagnetic impurities using finite temperature quantum Monte Carlo (FTQMC) method. A number of relevant macroscopic quantities calculated as a function of temperature T and impurity concentration are found to exhibit significantly renormalized behavior, a feature noted in many experiments. The uniform magnetic susceptibility χ0(T) for the impurity doped system shows a cusplike behavior followed by a sharp increase at lower temperatures, signaling the formation of impurity induced free magnetic moments, while it diminishes rapidly for the pure system. The spin correlations are found to increase in the vicinity of an impurity. To investigate the effect of nonmagnetic impurities on the spin wave modes in the system, spin wave velocity vsw is calculated as a function of impurity concentration. The result shows that vsw is reduced by nonmagnetic impurities, indicating softening of the modes. Simulations are performed slightly away from half filling and kinetic energy of the electrons in the neighborhood of an impurity site is calculated to study the interplay between impurities and holes. However, contrary to previous experimental observations on two dimensional lattices where nonmagnetic impurities reduce hole mobility, no noticeable effect of impurity on the mobility of the neighboring electrons is found in our calculation.
We investigate the single-band Hubbard model with random site energies in the strong-repulsion limit, as represented by the slave-boson formulation of the t-J model. It is essential to include the correlations between the slave-boson mean field and the disorder. This leads to the widening of the non-Fermi-liquid (``generalized Mott insulating'') region around half filling. In the Fermi-liquid regime we apply the renormalization-group method. The resulting phase diagram has superconducting, magnetic, and insulating phases. The disorder generally suppresses superconductivity and gives rise to the formation of localized magnetic moments.
Abstract The interplay between disorder and interaction, especially near metal insulator transitions, is a long‐standing question. We investigate in detail single impurities, in particular, the Friedel oscillations induced by them. We study the decay of the Friedel oscillations in the one‐dimensional Heisenberg and Hubbard model analytically using the bosonization technique and numerically using the density matrix renormalization group treatment (DMRG). For the Heisenberg chain, we confirm the predictions of conformal field theory and bosonization for small interaction, but near phase transitions deviations are found in form of vanishing or additional oscillations. For the Hubbard chain, we study the oscillations – in the density as well as in the magnetization – in the spin‐gap, charge‐gap, and Luttinger liquid phase. We find an exponential decay or a very slow algebraic decay of the oscillations in the gapped phases. In the Luttinger liquid phase, we concentrate on the question of logarithmic corrections (which occur also in the isotropic Heisenberg antiferromagnet). Differences in the behavior near a boundary compared to an impurity are pointed out. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Attractive non-local interactions jointly with repulsive local interaction in a microscopic modelling of electronic Fermi liquids generate a competition between an enhancement of the static charge susceptibility–ultimately signalling charge instability and phase separation–and its correlation induced suppression. We analyse this scenario through the investigation of the extended Hubbard model on a two-dimensional square lattice, using the spin rotation invariant slave-boson representation of Kotliar and Ruckenstein. The quasiparticle density of states, the renormalised effective mass and the Landau parameter F s 0 are presented, whereby the positivity of F s 0 – 1 constitutes a criterion for stability. Van Hove singularities in the density of states support possible charge instabilities. A (negative) next-nearest neighbour hopping parameter t' shifts their positions and produces a tendency towards charge instability even for low filling whereas the t' -controlled particle-hole asymmetry of the correlation driven effective mass is small. A region of instability on account of the attractive interaction V is identified, either at half filling in the absence of strong electronic correlations or, in the case of large on-site interaction U , at densities far from half filling.