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Physical Review B

Friedel oscillations in a Fermi liquid

George Simion, Gabriele F. Giuliani

Published Jul 19, 2005• 46 citations
Publisher

Abstract

The problem of the Friedel oscillations in two- and three-dimensional electron Fermi liquids is examined by means of the many-body local fields theory as aided by the most recent results of accurate numerical studies based on the quantum Monte Carlo method. Within linear response, an exact answer is obtained for the amplitude of the electron density distortion due to both short- and long-ranged impurity potentials. It is discussed how a measurement of the local environment of an impurity embedded in an otherwise homogeneous electron liquid can be used to characterize the systems as a Fermi liquid as well as to extract the magnitude of the static many-body corrections beyond the random phase approximation for wave vector equal to $2{k}_{F}$.

DOI
10.1103/physrevb.72.045127

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The problem of the Friedel oscillations in two- and three-dimensional electron Fermi liquids is examined by means of the many-body local fields theory as aided by the most recent results of accurate numerical studies based on the quantum Monte Carlo method. Within linear response, an exact answer is obtained for the amplitude of the electron density distortion due to both short- and long-ranged impurity potentials. It is discussed how a measurement of the local environment of an impurity embedded in an otherwise homogeneous electron liquid can be used to characterize the systems as a Fermi liquid as well as to extract the magnitude of the static many-body corrections beyond the random phase approximation for wave vector equal to 2kF2{k}_{F}2kF​.
The main topic of the present thesis is represented by the many-body effects which characterize the physical behavior of an electron liquid in various realizations. We begin by studying the problem of the response of an otherwise homogeneous electron liquid to the potential of an impurity embedded in its bulk. The most dramatic consequence of this perturbation is the existence of so called Friedel density oscillations. We present calculations of their amplitude valid in two as well as in three dimensions. The second problem we will discuss is that of the correlation effects in a three dimensional electron liquid in the metallic density regime. A number of quasiparticle properties are evaluated: the electron self-energy, the quasiparticle effective mass and the renormalization constant. We also present an analysis of the effective Landé g-factor as well as the compressibility. The effects of the Coulomb interactions beyond the random phase approximation have been treated by means of an approach based on the many-body local field factors theory and by utilizing the latest numerical results of Quantum Monte Carlo numerical simulations. The final chapter includes the results of our extensive work on various aspects regarding the two dimensional Fermi liquid in the presence of linear Rashba spin-orbit coupling. By using a number of many-body techniques, we have studied the interplay between spin-orbit coupling and electron-electron interaction. After proving an extension to the famous Overhauser Hartree-Fock instability theorem, a considerable amount of work will be presented on the problem of the density and spin response functions. For the study of the spin response, we will present the results of extensive numerical calculations based on the time dependent mean field theory approach.
We study Friedel oscillations and screening effects of the impurity potential in the Hubbard model. Electronic correlations are accounted for by solving the real-space dynamical mean-field theory equations using the continuous-time quantum Monte Carlo simulations at finite temperatures and using a homogeneous self-energy approximation with the numerical renormalization group at zero temperature. We find that in the Fermi-liquid phase both the amplitudes of Friedel oscillations and the screening charge decrease with increasing the interaction and follow the behavior of the Fermi-liquid renormalization factor. Inside the Mott insulator regime, the Friedel oscillations are absent but the residual screening charge remains finite.
We present a quantitative study of the quasiparticle properties of a three-dimensional electron Fermi liquid. Our approach is based on the theory of the many-body local field factors which we use to include vertex corrections associated with charge and spin fluctuations. Extensive use is made of the results of recent quantum Monte Carlo calculations. Several models for the wave-vector dependence of the spin-antisymmetric many-body local field factor ${G}_{\ensuremath{-}}$, for which no numerical results are currently available, are discussed and compared. Both the real and imaginary parts of the self-energy as well as the quasiparticle renormalization constant and the enhancement of the effective mass are calculated in the experimentally accessible range of electron densities. The results obtained by means of the on-shell approximation are critically compared with those given by a self-consistent solution of the Dyson equation. An ultraviolet catastrophe in the Coulomb-hole part of the self-energy is identified and a satisfactory resolution of this impasse is presented. The same many-body local field factors are also used to obtain the Landau interaction function. This allows us to obtain both the spin susceptibility and the proper compressibility of the system.
We numerically study Friedel Oscillations and screening effect around a single impurity in one- and two-dimensional interacting lattice electrons. The interaction between electrons is accounted for by using a momentum independent self-energy obeying the Luttinger theorem. It is observed in one-dimensional systems that the amplitude of oscillations is systematically damped with increasing the interaction while the period remains unchanged. The variation of screening charge with the impurity potential is discussed. We see that the screening charge is suppressed by the interactions. In case of two-dimensional systems the surface oscillations around the impurity are more localized with increasing the interactions.
We numerically study Friedel Oscillations and screening effect around a single impurity in one- and two-dimensional interacting lattice electrons. The interaction between electrons is accounted for by using a momentum independent self-energy obeying the Luttinger theorem. It is observed in one-dimensional systems that the amplitude of oscillations is systematically damped with increasing the interaction while the period remains unchanged. The variation of screening charge with the impurity potential is discussed. We see that the screening charge is suppressed by the interactions. In case of two-dimensional systems the surface oscillations around the impurity are more localized with increasing the interactions.
A deeper understanding of low-dimensional and small-scale electronic systems requires an accurate characterization of the many-electron effects. Based on the electron liquid (EL) model, these many-body effects in the three-dimensional (3D) and two-dimensional (2D) electronic systems are dealt going beyond the random phase approximation within the zero-temperature framework. The dielectric formulation of the many-body problem is recapitulated and the longitudinal dielectric function of the EL is obtained using the self-consistent local-field correction scheme, known as STLS, under a general spin-valley degeneracy. Extensive explicit expressions are provided for the use of other researchers. The performance of this formalism is compared in both 3D and 2D by the quantum Monte Carlo data and the pseudopotential approach introduced by Pines and co-workers. STLS is observed to be a highly satisfactory technique, with some reservations on the long-wavelength behaviour. Ground-state energy, correlation energy and the isothermal compressibility of the 2D EL are computed using a variety of approaches. Negative compressibility and overscreening are discussed in the light of the recent experiments.