By applying a magnetic field whose Zeeman energy exceeds the Kondo energy by an order of magnitude the ground state of the Friedel-Anderson impurity is a magnetic state. In recent years the author introduced the Friedel Artificially Inserted Resonance (FAIR) method to investigate impurity properties. Within this FAIR approach the magnetic ground state is derived. Its full excitation spectrum and the composition of the excitations is calculated and numerically evaluated. From the excitation spectrum the electron density of states is calculated. Majority and minority d-resonances are obtained. The width of the resonances is about twice as wide as the mean field theory predicts. This broadening is due to the fact that any change of the occupation of the d-state in one spin band changes the eigenstates in the opposite spin band and causes transitions in both spin bands. This broadening reduces the height of the resonance curve and therefore the density of states by a factor of two. This yields an intuitive understanding for a previous result of the FAIR approach that the critical value of the Coulomb interaction for the formation of a magnetic moment is twice as large as the mean field theory predicts.
It is shown that the calculation of the magnetic moment of a Friedel-Anderson impurity in mean-field theory is unreliable. A class of approximate solutions, which contains the mean-field solution as an element, is expressed in rotated Hilbert space and optimized. The optimal state has considerably lower energy than the mean field solution and requires almost twice the Coulomb exchange U to become magnetic. Since most moment calculations of magnetic impurities, for example the spin-density-functional theory, use the mean-field approximation the resulting magnetic moments have to be critically r…
Although the Kondo effect and the Kondo ground state of a magnetic impurity have been investigated for more than forty years it was until recently difficult if not impossible to calculate spatial properties of the ground state. In particular the calculation of the spatial distribution of the so-called Kondo cloud or even its existence have been elusive. In recent years a new method has been introduced to investigate the properties of magnetic impurities, the FAIR method, where the abbreviation stands for Friedel Artificially Inserted Resonance. The FAIR solution of the Friedel-Anderson and the…
An approximate groundstate of the Anderson-Friedel impurity problem is presented in a very compact form. It requires solely the optimization of two localized electron states and consists of four Slater states (Slater determinants). The resulting singlet ground state energy lies far below the Anderson mean field solution and agrees well with the numerical results by Gunnarsson and Schoenhammer, who used an extensive 1/N_{f}-expansion for a spin 1/2 impurity with double occupancy of the impurity level. PACS: 85.20.Hr, 72.15.Rn
We study the effect of impurity scattering effect in black phosphorurene (BP) in this work. For single impurity, we calculate impurity induced local density of states (LDOS) in momentum space numerically based on tight-binding Hamiltonian. In real space, we calculate LDOS and Friedel oscillation analytically. LDOS shows strong anisotropy in BP. Many impurities in BP are investigated using $T$-matrix approximation when the density is low. Midgap states appear in band gap with peaks in DOS. The peaks of midgap states are dependent on impurity potential. For finite positive potential, the impurit…
We show that Friedel oscillations (FO) in grapehene are strongly affected by the chirality of electrons in this material. In particular, the FO of the charge density around an impurity show a faster, $1/r^3$, decay than in conventional 2D electron systems and do not contribute to a linear temperature-dependent correction to the resistivity. In contrast, the FO of the exchange field which surrounds atomically sharp defects breaking the hexagonal symmetry of the honeycomb lattice lead to a negative linear T dependence of the resistivity.
Recently Affleck et al. derived the existence of Friedel oscillations in the presence of a Kondo impurity. They supported their analytic derivation by numerical calculations using Wilson's renormalization approach (NRG). In this paper the size of the Friedel oscillations is calculated with the FAIR method (Friedel Artificially Inserted Resonance) which has been recently developed. The results of NRG and FAIR are compared. The development of Friedel oscillations with a phase shift of pi/2 outside of the Kondo radius is confirmed.
This work addresses the problem of elastic scattering through a localized impurity in a one-dimensional crystal with sublattice freedom degrees. The impurity yields long-range interferences in the local density of states known as Friedel oscillations. Here, we show that the internal degrees of freedom of Bloch waves are responsible for a geometrical phase shift in Friedel oscillations. The Fourier transform of the energy-resolved interference pattern reveals a topological property of this phase shift, which is intrinsically related to the Bloch band structure topology in the absence of impurit…
We present detailed numerical studies of the magnetic anisotropy energy of a magnetic impurity near the surface of metallic hosts (Au and Cu), that we describe in terms of a realistic tight-binding surface Green's function technique. We study the case when spin-orbit coupling originates from the d-band of the host material and we also investigate the case of a strong local spin-orbit coupling on the impurity itself. The splitting of the impurity's spin-states is calculated to leading order in the exchange interaction between the impurity and the host atoms using a diagrammatic Green's function…
The Friedel oscillations caused due to an impurity located at one edge of a disordered interacting quantum wire are calculated numerically. The electron density in the system's ground state is determined using the DMRG method, and the Friedel oscillations data is extracted using the density difference between the case in which the wire is coupled to an impurity and the case where the impurity is uncoupled. We show that the power law decay of the oscillations occurring for an interacting clean 1D samples described by Luttinger liquid theory, is multiplied by an exponential decay term due to the…
We analyze the consequences of a first-order (in the effective Kondo coupling) inter-impurity correlation present in the Two-Impurity Anderson Hamiltonian. This correlation generates a pair of Kondo Doublet states which are responsible for the first (higher energy) Kondo stage of these systems. Applied to systems of quantum dots in a semiconductor heterolayer, these Doublets predict a mainly ferromagnetic dot-dot spin correlation which is different than the expected from the second-order RKKY interaction. In order to effectively screen both dots, a parallel alignment of the dot-spins is favore…
We examine the Friedel sum rule which states that the "excess charge" due to a single impurity potential in a metal is equal to a sum of phase shifts for scatterings of electrons by the impurity. For finite volume, the ``excess charge" is given by the difference between total numbers of levels in the Fermi sea with and without the impurity potential. However, a sequence of the "excess charge" for finite volume is not necessarily bounded in the infinite volume limit, as was pointed out by Kirsch. In order to circumvent this difficulty, we define "excess charge" directly for the infinite volume.…
The strongly correlated two-electron transport in one-dimensional channel coupled with an Anderson-type impurity is solved exactly via a Bethe ansatz approach. We show that the transport properties are fundamentally different for spin singlet and triplet states, thus the impurity acts as a novel filter that operates based on the total spin angular momentum of the electron pairs, but not individual spins. The filter provides a deterministic generation of electron entanglement in spin, as well as energy and momentum space.
In a recent Comment, Kolf et al. (cond-mat/0503669) state that our analysis of the Fano resonance for Anderson impurity systems [Luo et al., Phys. Rev. Lett 92, 256602 (2004)] is incorrect. Here we want to point out that their comments are not based on firm physical results and their criticisms are unjustified and invalid.
Recent developments in the numerical renormalization group (NRG) allow the construction of the full density matrix (FDM) of quantum impurity models (see A. Weichselbaum and J. von Delft) by using the completeness of the eliminated states introduced by F. B. Anders and A. Schiller (2005). While these developments prove particularly useful in the calculation of transient response and finite temperature Green's functions of quantum impurity models, they may also be used to calculate thermodynamic properties. In this paper, we assess the FDM approach to thermodynamic properties by applying it to t…
We compute exactly the low-energy single-electron Green's function, the impurity and electron self-energies, and the resistivity for the two-channel Anderson impurity model. These results are obtained by exploiting the boundary conformal field theory identified from the Bethe Ansatz solution of the model. Using that solution we can make contact with the parameters of the original Hamiltonian and provide the detailed crossover between the two integer valence limits. Our results generalize those obtained previously in the context of the two-channel Kondo model.
We investigate the local density of states and Friedel oscillation in graphene around a well localized impurity in Born approximation. In our analytical calculations Green's function technique has been used taking into account both the localized atomic wavefunctions in a tight-binding scheme and the corresponding symmetries of the lattice. As a result we obtained long wavelength oscillations in the density of electrons with long range behavior proportional to the inverse square of the distance from the impurity. These leading oscillations are out of phase on nearby lattice sites (in fact for a…
We analyze the spectrum of electron density oscillations in an interacting one-dimensional electron system with an impurity. The system's inhomogeneity is characterized by different values of Fermi wave vectors $k_F=k_{L/R}$ on left/right side of the scatterer, leading to a Landauer dipole formation. We demonstrate, that while in the noninteracting system the Friedel oscillations possess only one periodicity related to the local $k_F$, say $k_L$ on the left side, the interplay of the interactions and the Landauer dipole generates an additional peak in the spectrum of density oscillations at th…
Transient and steady state currents through dc-biased quantum impurity models beyond the linear response regime are of considerable interest, both from an experimental and a theoretical point of view. Here we present a new analytical approach for the calculation of such currents based on the flow equation method (method of infinitesimal unitary transformations). Specifically, we analyze the Anderson impurity model in its mixed valence regime where the coupling to the leads is switched on suddenly at time $t=0$. We observe the real time buildup of the current until it reaches its steady state l…
We reobtain the Kondo-Doublet interaction by means of the Brillouin-Wigner Perturbation theory. By applying the same method to the single impurity case we show that the Kondo-Doublet interaction is a direct consequence of the Kondo screening cloud. We fully confirm our previous results on this novel interaction. In particular, we found that for values of the system parameters typical of semiconductor Quantum Dots heterostructures, the ferromagnetic Kondo-Doublet interaction dominates over the RKKY one.
Unitary limit for model point scatterers in graphene is known to reveal low-energy resonances. The same limit could be achieved from hybridization of band electrons with the localized impurity level positioned in the vicinity of the Fermi level. The finite size defects represent an easier realization of the effective unitary limit, occurring when the Fermi wavelength induced by the potential becomes of the order of the size of the defect. We calculate the induced electron density and find two signatures of a strong impurity, independent of its specific realization. The dependence of the impuri…
We study the Anderson model in which a configuration with a doublet is hybridized with another with a singlet and a triplet. We calculate the conductance through the system as a function of temperature and bias voltage, near the quantum critical line for which the system is exactly solvable. The results explain recent transport measurements in a single-molecule quantum dot.
When a single resonator is coupled to a continuous spectrum one obtains a resonance of finite half-width. Such a resonance is known in many fields of physics. The Friedel resonance is an example where a d-impurity is dissolved in a simple metal. If two resonators are coupled to the continuous spectrum the resonances interfere. For identical coupling and frequencies one obtains two effective resonances. The effective coupling of one of them to the continuum can be tuned to zero yielding a delta-like resonance.
Two opposite chiralities of Dirac electrons in a 2D graphene sheet modify the Friedel oscillations strongly: electrostatic potential around an impurity in graphene decays much faster than in 2D electron gas. At distances $r$ much larger than the de Broglie wavelength, it decays as $1/r^3$. Here we show that a weak uniform magnetic field affects the Friedel oscillations in an anomalous way. It creates a field-dependent contribution which is {\em dominant} in a parametrically large spatial interval $p_0^{-1}\lesssim r\lesssim k_Fl^2$, where $l$ is the magnetic length, $k_F$ is Fermi momentum and…
Quantum transport is studied for the nonequilibrium Anderson impurity model at zero temperature employing the multilayer multiconfiguration time-dependent Hartree theory within the second quantization representation (ML-MCTDH-SQR) of Fock space. To adress both linear and nonlinear conductance in the Kondo regime, two new techniques of the ML-MCTDH-SQR simulation methodology are introduced: (i) the use of correlated initial states, which is achieved by imaginary time propagation of the overall Hamiltonian at zero voltage and (ii) the adoption of the logarithmic discretization of the electronic …
The low-energy physics of rhombohedral $N$-layer graphene mainly arises on the external layers, where most of the π electrons are located. Their Bloch band structure defines a two-band semimetal; the dispersion relation scales as $\pm q^{N}$ with the momentum norm $q$ in the vicinity of two nonequivalent valleys. In this paper, we address the problem of elastic scattering through a localized impurity located either on the surface of the material or within the bulk, and focus on the quantum interferences it induces on the two external layers. It is apprehended in the framework of a $T$-matrix a…
We analyze the spectrum of the electric-current autocorrelation function (noise power) in the Anderson impurity model biased by a finite transport voltage. Special emphasis is placed on the interplay of non-equilibrium effects and electron-electron interactions. Analytic results are presented for a perturbation expansion in the interaction strength $U$. Compared to the non-interacting setup we find a suppression of noise for finite frequencies in equilibrium and an amplification in non-equilibrium. Furthermore, we use a diagrammatic resummation scheme to obtain non-perturbative results in the …
We present an extension of the non-crossing approximation (NCA), which is widely used to calculate properties of Anderson impurity models in the limit of infinite Coulomb repulsion $U\to\infty$, to the case of finite $U$. A self-consistent conserving pseudo-particle representation is derived by symmetrizing the usual NCA diagrams with respect to empty and doubly occupied local states. This requires an infinite summation of skeleton diagrams in the generating functional thus defining the ``Symmetrized finite-U NCA'' (SUNCA). We show that within SUNCA the low energy scale $T_K$ (Kondo temperatur…
We propose a realization of the two-impurity Anderson model in a double quantum-dot device. When charge transfer between the dots is suppressed the system exhibits a quantum phase transition, controlled by a surface of non-Fermi liquid fixed points parameterized by the charge valences of the dots. Employing conformal field theory techniques, we identify the scaling exponents that govern transport and thermodynamics close to criticality. We also determine the dynamical exponents that set the time scale for buildup of the non-Fermi liquid state after the system is suddenly shifted into the criti…
The Distributional Exact Diagonalization (DED) scheme is applied to the description of Kondo physics in the Anderson impurity model. DED maps Anderson's problem of an interacting impurity level coupled to an infinite bath onto an ensemble of finite Anderson models, each of which can be solved by exact diagonalization. An approximation to the self-energy of the original infinite model is then obtained from the ensemble averaged self-energy. Using Friedel's sum rule, we show that the particle number constraint, a central ingredient of the DED scheme, ultimately imposes Fermi liquid behavior on t…
We investigate the dynamical and steady-state spin response of the nonequilibrium Anderson model to magnetic fields, bias voltage, and temperature using a numerically exact method combining a bold-line quantum Monte Carlo technique with the memory function formalism. We obtain converged results in a range of previously inaccessible regimes, in particular the crossover to the Kondo domain. We provide detailed predictions for novel nonequilibrium phenomena, including non-monotonic temperature dependence of observables at high bias voltage and oscillatory quench dynamics at high magnetic fields.
We present a microscopic Fermi-liquid view on the low-energy transport through an Anderson impurity with $N$ discrete levels, at arbitrary electron filling $N_d$. It is applied to nonequilibrium current fluctuations, for which the two-quasiparticle collision integral and the three-body correlations that determine the quasiparticle energy shift play important roles. Using the numerical renormalization group up to $N=6$, we find that for strong interactions the three-body fluctuations are determined by a single parameter other than the Kondo energy scale in a wide filling range $1 \lesssim N_d \…
The bosonic single-impurity Anderson model (B-SIAM) is studied to understand the local dynamics of an atomic quantum dot (AQD) coupled to a Bose-Einstein condensation (BEC) state, which can be implemented to probe the entanglement and the decoherence of a macroscopic condensate. Our recent approach of the numerical renormalization group (NRG) calculation for the B-SIAM revealed a zero-temperature phase diagram, where a Mott phase with local depletion of normal particles is separated from a BEC phase with enhanced density of the condensate. As an extension of the previous work, we present the c…
We show how the density-matrix numerical renormalization group (DM-NRG) method can be used in combination with non-Abelian symmetries such as SU(N), where the decomposition of the direct product of two irreducible representations requires the use of a so-called outer multiplicity label. We apply this scheme to the SU(3) symmetrical Anderson model, for which we analyze the finite size spectrum, determine local fermionic, spin, superconducting, and trion spectral functions, and also compute the temperature dependence of the conductance. Our calculations reveal a rich Fermi liquid structure.
An exact relation between the conductance maximum $G_0$ at zero temperature and a ratio of lead densities is derived within the framework of the single impurity Anderson model: $G_0={\mathfrak R}[n] \frac{2e^2}{h}$, where ${\mathfrak R}[n]=4ΔN_{{\cal L},x} ΔN_{{\cal R},x}/(ΔN_{{\cal L},x}+ΔN_{{\cal R},x})^2$ and $ΔN_{{\cal L},x}$, $ΔN_{{\cal R},x}$ denote the excess density in the left/right lead at distance $x$ due to the presence of the impurity at the origin, $x=0$. The relation constitutes a parameter-free expression of the conductance of the model in terms of the ground state density that…
Friedel oscillations (FO) of electron density caused by a delta-like neutral impurity in two-dimensional (2D) systems in a magnetic field are calculated. Three 2D cases are considered: free electron gas, monolayer graphene and group-VI dichalcogenides. An exact form of the renormalized Green's function is used in the calculations, as obtained by a summation of the infinite Dyson series and regularization procedure. Final results are valid for large ranges of potential strengths $V_0$, electron densities $n_e$, magnetic fields $B$ and distances from the impurity $r$. Realistic models for the im…
We consider inelastic scattering of localized magnetic moments coupled with the electrons on the surface. We argue that spin-inelastic transitions of the magnetic impurities generate oscillations at a momentum $k$, corresponding to the inelastic mode, in the second derivative of the current with respect to voltage $d^2I/dV^2$. These oscillations are similar in nature to Friedel oscillations. Inelastic Friedel oscillations, which were previously proposed for spin-unpolarized set-up, is here extended for spin-polarized systems. We propose to use scanning tunneling microscope to measure spin-inel…
We study the Friedel oscillations induced by a localized impurity in anisotropic graphene. We focus on the limit when the two inequivalent Dirac points merge. We find that in this limit the Friedel oscillations manifest very peculiar features, such as a strong asymmetry and an atypical inverse square-root decay. Our calculations are performed using both a T-matrix approximation and a tight-binding exact diagonalization technique. They allow us to obtain numerically the local density of states as a function of energy and position, as well as an analytical form of the Friedel oscillations in the…
Electrons mediate many of the interactions between atoms in a solid. Their propagation in a material determines its thermal, electrical, optical, magnetic and transport properties. Therefore, the constant energy contours characterizing the electrons, in particular the Fermi surface, have a prime impact on the behavior of materials. If anisotropic, the contours induce strong directional dependence at the nanoscale in the Friedel oscillations surrounding impurities. Here we report on giant anisotropic charge density oscillations focused along specific directions with strong spin-filtering after …
Weyl semimetals are prominent examples of topologically protected quantum matter. These materials are the three-dimensional counterparts of graphene and great efforts are being devoted to achieve a thorough understanding of their fundamental physics. In this work, we aim at contributing to this end by discussing the effect of a single magnetic impurity in Weyl semimetals as a first step towards considering a larger number of impurities. We find that resonances appear in the local density of states with a Friedel-like behaviour, oscillating as a function of distance. By studying the spin-resolv…
Friedel's sum rule provides an explicit expression for a conductance functional, $\mathcal{G}[n]$, valid for the single impurity Anderson model at zero temperature. The functional is special because it does not depend on the interaction strength $U$. As a consequence, the Landauer conductance for the Kohn-Sham (KS) particles of density functional theory (DFT) coincides with the true conductance of the interacting system. The argument breaks down at temperatures above the Kondo scale, near integer filling, $n_{\text{d}σ}\approx 1/2$ for spins $σ{=}\uparrow\downarrow$. Here, the true conductance…
We investigate the effect of assisted hopping in the Anderson impurity model. We use the flow equation method, which, by means of unitary transformations, generates a sequence of Hamiltonians in order to eliminate the assisted hopping terms. This approach yields a renormalized on-site energy $ε_d^*$, a renormalized correlation energy $U^*$ and other terms, which include pair hopping. For some parameter values, the initial Hamiltonian flows towards an attractive Anderson model. We argue that this result implies a tendency towards local pairing fluctuations.
Based on the finite $U$ slave boson method, we have investigated the effect of Rashba spin-orbit(SO) coupling on the persistent charge and spin currents in mesoscopic ring with an Anderson impurity. It is shown that the Kondo effect will decrease the magnitude of the persistent charge and spin currents in this side-coupled Anderson impurity case. In the presence of SO coupling, the persistent currents change drastically and oscillate with the strength of SO coupling. The SO coupling will suppress the Kondo effect and restore the abrupt jumps of the persistent currents. It is also found that a …
We consider a single impurity Anderson model (SIAM) in which the quantum dot(QD) is strongly coupled to a phonon bath in polaron regime. This coupling results in an effective e-e attraction. By computing the self energies using a current conserving approximation which is up to second order in this effective attraction, we show that if the interaction is strong enough, in non particle-hole(PH) symmetric case, the system would be bi-stable and we have hysteresis loop in the I-V characteristic. Moreover, the system shows negative differential conductance in some bias voltage intervals.
We theoretically investigate the spin resolved Friedel oscillation (FO) and quasiparticle interference (QPI) in graphene induced by an Anderson impurity. Once the impurity becomes magnetic, the resulted FO becomes spin dependent, which gives rise to a local magnetic moment oscillation with an envelop decaying as $r^{-2}$ in real space in the doping cases. Meanwhile, at half filling, the charge density and local magnetic moment will not oscillate but decay as $r^{-3}$. Such spin resolved FO has both sublattice and spin asymmetry. Interestingly, the local magnetic moment decay at half filling on…
We investigate the mean-field phase diagram of the Anderson impurity model out of equilibrium. Generalising the unrestricted Hartree-Fock approach to the non-equilibrium situation we derive and analyse the system of equations defining the critical surface separating the magnetic regime from the non-magnetic one. An exact analytic solution for the phase boundary as a function of the applied voltage is found in the symmetric case. Surprisingly, we find that as soon as there is an asymmetry, even small, between the contacts, no finite voltage is able to destroy the magnetic regime which persists …
We study spin-entanglement of the quasiparticles of the local Fermi liquid excited in nonlinear current through a quantum dot described by the Anderson impurity model with two degenerate orbitals coupled to each other via an exchange interaction. Applying the renormalized perturbation theory, we obtain the precise form of the cumulant generating function and cross-correlations for the currents with spin angled to arbitrary directions, up to third order in the applied bias voltage. It is found that the exchange interaction gives rise to spin-angle dependency in the cross-correlation between the…
We discuss the transient effects in the Anderson impurity model that occur when two fermionic continua with finite bandwidths are instantaneously coupled to a central level. We present results for the analytically solvable noninteracting resonant level system first and then consistently extend them to the interacting case using the conventional perturbation theory and recently developed nonequilibrium Monte Carlo simulation schemes. The main goal is to gain an understanding of the full time-dependent nonlinear current-voltage characteristics and the population probability of the central level.…
We study a series-coupled double quantum dot in the Kondo regime modeled by the two-impurity Anderson model and find a new conduction-band mediated superexchange interaction that competes with Kondo physics in the strong Coulomb interaction limit. Our numerical renormalization group results, complemented with the higher-order Rayleigh-Schrödinger perturbation theory, show that the novel exchange mechanism leads to clear experimental consequences that can be checked in transport measurements through double quantum dots.
In this work, we investigate the characteristics of the electric current in the so-called symmetric Anderson impurity model. We study the nonequilibrium model using two complementary approximate methods, the perturbative quantum master equation approach to the reduced density matrix, and a self-consistent equation of motion approach to the nonequilibrium Green's function. We find that at a particular symmetry point, an interacting Anderson impurity model recovers the same steady-state current as an equivalent non-interacting model, akin a two-band resonant level model. We show this in the Coul…
The magnetic moment of a single impurity atom in a finite free electron gas is studied in a combined x-ray magnetic circular dichroism spectroscopy and density functional theory study of size-selected free chromium-doped gold clusters. The observed size-dependence of the local magnetic moment can essentially be understood in terms of the Anderson impurity model. Electronic shell closure in the host metal minimizes the interaction of localized impurity states with the confined free electron gas and preserves the full magnetic moment of $\unit[5]{μ_B}$ in $\mathrm{CrAu}_{2}^{+}$ and $\mathrm{CrA…
We study the interacting, symmetrically coupled single impurity Anderson model. By employing the nonequilibrium Green's function formalism, we establish an exact relationship between the steady-state charge current flowing through the impurity (dot) and its occupation. We argue that the steady state current-occupation relation can be used to assess the consistency of simulation techniques, and identify spurious transport phenomena. We test this relation in two different model variants: First, we study the Anderson-Holstein model in the strong electron-vibration coupling limit using the polaron…
We apply the recently proposed quasi-classical approach for a second quantized many-electron Hamiltonian in Cartesian coordinates [J. Chem. Phys. 137, 154107 (2012)] to correlated nonequilibrium quantum transport. The approach provides accurate results for the resonant level model for a wide range of temperatures, bias and gate voltages, correcting for the flaws of our recently proposed mapping using action-angle variables. When electron-electron interactions are included, higher order schemes are required to map the two-electron integrals, leading to semi-quantitative results for the Anderson…
