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.

Aug 14, 20166 citations

Real-space dynamical mean-field theory of Friedel oscillations in strongly correlated electron systems

Banhi Chatterjee, Jan Skolimowski, Karol Makuch +1 more

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 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.

arXiv:1807.08566Physical review. B./Physical review. BSep 10, 20199 citations

Impurities and other defects in correlated lattice electrons: Friedel oscillations and interference patterns

Banhi Chatterjee, Jan Skolimowski, Krzysztof Byczuk

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.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.

arXiv:2007.11443Physical review. B./Physical review. BJun 21, 20222 citations

Friedel oscillations and interference patterns from multiple impurities in free fermions in continuous space and in correlated lattice electrons

Banhi Chatterjee, Jan Skolimowski, Krzysztof Byczuk

We study the interference patterns in the Friedel oscillations (FO) due to the scattering off either two or multiple impurities and scattering off extended inhomogeneities both in the non-interacting and two-dimensional lattice systems of interacting fermions. Correlations are accounted for by using an approximate method based on the real-space dynamical mean-field theory. 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 interaction increase does not shift the position of interference fringes but only reduces their intensities. A comparison with the single impurity studies clearly shows complex patterns in FO induced by the additional scattering potentials. In the case of an extended step potential the system becomes more homogeneous when the interaction increases. FO and interference patterns are not present in the Mott insulating phase in the single and the many impurity models. Our theoretical study provides promising initial insights and motivate a further realistic modeling to investigate the role of interstitial defects, embedded impurities, ad-atoms on the surfaces, and surface irregularities in materials with different degrees of electronic correlation. For a complete description we also present analytical and numerical results of FO for non-interacting particles moving in a two and three dimensional continuous spaces. In the diluted impurity limit we derive results for FO due to scattering off many impurities, which are generalization of the original Friedel formula.We study the interference patterns in the Friedel oscillations (FO) due to the scattering off either two or multiple impurities and scattering off extended inhomogeneities both in the non-interacting and two-dimensional lattice systems of interacting fermions. Correlations are accounted for by using an approximate method based on the real-space dynamical mean-field theory. 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 interaction increase does not shift the position of interference fringes but only reduces their intensities. A comparison with the single impurity studies clearly shows complex patterns in FO induced by the additional scattering potentials. In the case of an extended step potential the system becomes more homogeneous when the interaction increases. FO and interference patterns are not present in the Mott insulating phase in the single and the many impurity models. Our theoretical study provides promising initial insights and motivate a further realistic modeling to investigate the role of interstitial defects, embedded impurities, ad-atoms on the surfaces, and surface irregularities in materials with different degrees of electronic correlation. For a complete description we also present analytical and numerical results of FO for non-interacting particles moving in a two and three dimensional continuous spaces. In the diluted impurity limit we derive results for FO due to scattering off many impurities, which are generalization of the original Friedel formula.

Jul 22, 20200 citations

Friedel oscillations in Luttinger liquids

Reinhold Egger, Hermann Grabert

We study the density disturbance of a correlated 1D electron liquid in the presence of a scatterer or a barrier. The 2k_F-periodic density profile away from the barrier (Friedel oscillation) is computed for arbitrary electron--electron interaction and arbitrary impurity strength. We find that in presence of correlations, the Friedel oscillation decays slower than predicted by Fermi liquid theory. In the case of a spinless Luttinger liquid characterized by an interaction constant g<1, the asymptotic decay of the Friedel oscillation is x^-g. For a weak scatterer, the decay is even slower at small-to-intermediate distances from the impurity, with a crossover to the asymptotic x^-g law.We study the density disturbance of a correlated 1D electron liquid in the presence of a scatterer or a barrier. The 2k_F-periodic density profile away from the barrier (Friedel oscillation) is computed for arbitrary electron--electron interaction and arbitrary impurity strength. We find that in presence of correlations, the Friedel oscillation decays slower than predicted by Fermi liquid theory. In the case of a spinless Luttinger liquid characterized by an interaction constant g<1, the asymptotic decay of the Friedel oscillation is x^-g. For a weak scatterer, the decay is even slower at small-to-intermediate distances from the impurity, with a crossover to the asymptotic x^-g law.

arXiv:cond-mat/9604026Apr 4, 19960 citations

Friedel oscillations in a Fermi liquid

George Simion, Gabriele F. Giuliani

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 $2{k}_{F}$ .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 $2{k}_{F}$.

Physical Review BJul 19, 200546 citations

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