Friedel Sum Rule Research Articles

Form factor of the electron density of an anion specifically adsorbed on metal surface in an electrolyte

The character of distribution of electron density over the proximity of a halide anion specifically adsorbed at the s,p-metal-electrolyte solution interface boundary was considered. An assumption was made that the physical nature of the specific bonding of the anion is caused by mixing of electron waves of free electrons in the metal and the valent state of the anion as the electrons resonantly overcome the potential barrier between the anion and the metal. The physical (dissipative quantum) mechanism of microscopic processes is described using the Anderson impurity model, the Friedel sum rule, and the Parr conception of equalization of electronegativity values that determine the partial transfer of electron charge from the anion to the metal and the emergence of localized dipole at the interphase boundary. The equations renormalizing the microscopic parameters of the adsorption event to macroscopic state functions of the adsorption phase on an electrode were obtained. The chemical potential of the halide anion specifically adsorbed from electrolyte solution on an uncharged electrode is estimated. The mechanism under consideration explains the details of the dependences of polarization parameters of the electrode on anion and metal nature.

Extremely correlated Fermi liquid study of theU=∞Anderson impurity model

We apply the recently developed extremely correlated Fermi liquid (ECFL) theory to the Anderson impurity model, in the extreme correlation limit $U\ensuremath{\rightarrow}\ensuremath{\infty}$. We develop an expansion in a parameter $\ensuremath{\lambda}$, related to ${n}_{d}$, the average occupation of the localized orbital, and find analytic expressions for the Green's functions to $O({\ensuremath{\lambda}}^{2})$. These yield the impurity spectral function and also the self-energy $\ensuremath{\Sigma}(\ensuremath{\omega})$ in terms of the two self-energies of the ECFL formalism. The imaginary parts of the latter have roughly symmetric low-energy behavior ($\ensuremath{\propto}{\ensuremath{\omega}}^{2}$), as predicted by Fermi liquid theory. However, the inferred impurity self-energy ${\ensuremath{\Sigma}}^{\ensuremath{'}\ensuremath{'}}(\ensuremath{\omega})$ develops asymmetric corrections near ${n}_{d}\ensuremath{\rightarrow}1$, leading in turn to a strongly asymmetric impurity spectral function with a skew towards the occupied states. Within this approximation, the Friedel sum rule is satisfied but we overestimate the quasiparticle weight $z$ relative to the known exact results, resulting in an overbroadening of the Kondo peak. Upon scaling the frequency by the quasiparticle weight $z$, the spectrum is found to be in reasonable agreement with numerical renormalization group results over a wide range of densities.

Density functional theory with exact XC potentials: Lessons from DMRG studies and exactly solvable models

Density functional theory in the Kohn‐Sham formulation is the most successful method in chemistry and physics when it comes to predicting crystal and molecular structures. Very frequently it is also used with benefit for estimating the corresponding electronic dispersion relations. Therefore, it is not surprising that computations have been attempted of observables that, strictly speaking, are beyond those protected by the Hohenberg‐Kohn theorems. The most infamous one of them is the conductance of single molecules. In this article we offer a brief overview of recent developments that justify such transport studies in situations where transport is dominated by a single orbital. In such situations the Friedel sum rule establishes a relation between conductance and ground‐state density that is free of microscopic parameters, such as the interaction strength, and therefore can provide a rigorous link between Kohn‐Sham transport and the physical observables. What happens in more general situations is also discussed.

The stopping of heavy ions in the low-to-intermediate energy range: The apparent velocity threshold

We present a non-linear study of the energy loss of heavy ions in solids, which is based on the transport cross section (TCS) and the extension of the Friedel sum rule (EFSR) for moving ions. We apply this approach to study the velocity dependence of the energy loss of heavy ions in the energy region below the stopping power maximum. With this formulation we are able to explain some striking effects in the energy loss of heavy ions which have been experimentally observed long time ago (Brown and Moak (1972) [14]), but have not been explained so far by the existing theoretical models: the deviations from the proportionality with ion velocity (predicted by alternative models in the low energy range), and the “apparent velocity threshold”.

Second-order Born approximation for the scattering phase shifts: Application to the Friedel sum rule

Screening effects are important to understand various aspects of ion–solid interactions and, in particular, play a crucial role in the stopping of ions in solids. In this paper the phase shifts and scattering amplitudes for the quantum-mechanical elastic scattering within up to the second-order Born (B2) approximation are revisited for an arbitrary spherically-symmetric electron–ion interaction potential. The B2 phase shifts and scattering amplitudes are then used to derive the Friedel sum rule (FSR) involving the second-order Born corrections. This results in a simple equation for the B2 perturbative screening parameter of an impurity ion immersed in a fully degenerate electron gas which, as expected, turns out to depend on the ion atomic number Z1 unlike the first-order Born (B1) screening parameter reported earlier by some authors. Furthermore, our analytical results for the Yukawa, hydrogenic, Hulthén, and Mensing potentials are compared, for both positive and negative ions and a wide range of one-electron radii, to the exact screening parameters calculated self-consistently by imposing the FSR requirement. It is shown that the B2 screening parameters agree excellently with the exact values at large and moderate densities of the degenerate electron gas, while at lower densities they progressively deviate from the exact numerical solutions but are nevertheless more accurate than the prediction of the B1 approximation. In addition, a simple Padé approximant to the Born series has been developed that improves the performance of the perturbative FSR for any negative ion as well as for Z1=+1.

Spin-polarized conductance in double quantum dots: Interplay of Kondo, Zeeman, and interference effects

We study the effect of a magnetic field in the Kondo regime of a double-quantum-dot system consisting of a strongly correlated dot (the ``side dot'') coupled to a second, noninteracting dot that also connects two external leads. We show, using the numerical renormalization group, that application of an in-plane magnetic field sets up a subtle interplay between electronic interference, Kondo physics, and Zeeman splitting with nontrivial consequences for spectral and transport properties. The value of the side-dot spectral function at the Fermi level exhibits a nonuniversal field dependence that can be understood using a form of the Friedel sum rule that appropriately accounts for the presence of an energy- and spin-dependent hybridization function. The applied field also accentuates the exchange-mediated interdot coupling, which dominates the ground state at intermediate fields leading to the formation of antiparallel magnetic moments on the dots. By tuning gate voltages and the magnetic field, one can achieve complete spin polarization of the linear conductance between the leads, raising the prospect of applications of the device as a highly tunable spin filter. The system's low-energy properties are qualitatively unchanged by the presence of weak on-site Coulomb repulsion within the second dot.

Controlled Dephasing of an Electron Interferometer with a Path Detector at Equilibrium

Controlled dephasing of electrons, via "which path" detection, involves, in general, coupling a coherent system to a current driven noise source. However, here we present a case in which a nearly isolated electron puddle within a quantum dot, at thermal equilibrium and in millikelvin range temperature, fully dephases the interference in a nearby electronic interferometer. Moreover, the complete dephasing is accompanied by an abrupt π phase slip, which is robust and nearly independent of system parameters. Attributing the robustness of the phenomenon to the Friedel sum rule--which relates a system's occupation to its scattering phases--proves the universality of this powerful rule. The experiment allows us to peek into a nearly isolated quantum dot, which cannot be accessed via conductance measurements.

The Spectral Shift Function and the Friedel Sum Rule

We study the relationship between the spectral shift function and the excess charge in potential scattering theory. Although these quantities are closely related to each other, they have been often formulated in different settings so far. Here, we first give an alternative construction of the spectral shift function, and then we prove that the spectral shift function thus constructed yields the Friedel sum rule.

Stopping power of Zn for heavy ions

We present stopping power measurements of Zn for C and O ions and compare them with a theoretical description given by the Transport Cross Section - Extended Friedel Sum Rule (TCS-EFSR) for the valence electrons, and two different models for the inner-shells: the Shellwise Local Plasma Approximation (SLPA) and the CasP approach. The SLPA, which successfully applies to projectiles from H to B, is slightly high for C ions and clearly overestimates the data for O ions. On the other hand, total stopping results using the CasP description for the inner-shells show good agreement with the data for C and O ions, and also with the SRIM predictions.

Fermi liquid approach to the quantumRCcircuit: Renormalization group analysis of the Anderson and Coulomb blockade models

We formulate a general approach for studying the low-frequency response of an interacting quantum dot connected to leads in the presence of oscillating gate voltages. The energy dissipated is characterized by the charge relaxation resistance, which under the loose assumption of Fermi liquid behavior at low energy, is shown to depend only on static charge susceptibilities. The predictions of the scattering theory are recovered in the noninteracting limit while the effect of interactions is simply to replace densities of states by charge susceptibilities in formulas. In order to substantiate the Fermi liquid picture in the case of a quantum RC geometry, we apply a renormalization group analysis and derive the low-energy Hamiltonian for two specific models: the Anderson and the Coulomb blockade models. The Anderson model is shown, using a field theoretical approach based on Barnes slave bosons, to map onto the Kondo model. We recover the well-known expression of the Kondo temperature for the asymmetric Anderson model and compute the charge susceptibility. The Barnes slave bosons are extended to the Coulomb blockade model where the renormalization-group analysis can be carried out perturbatively up to zero energy. All calculations agree with the Fermi liquid nature of the low-energy fixed point and satisfy the Friedel sum rule.

General derivation of the Green's functions for the atomic approach of the Anderson model: application to a single electron transistor (SET)

We consider the cumulant expansion of the periodic Anderson model (PAM) in the case of a finite electronic correlation U, employing the hybridization as perturbation, and obtain a formal expression of the exact one-electron Green's function (GF). This expression contains effective cumulants that are as difficult to calculate as the original GF, and the atomic approach consists in substituting the effective cumulants by the ones that correspond to the atomic case, namely by taking a conduction band of zeroth width and local hybridization. In a previous work (T. Lobo, M. S. Figueira, and M. E. Foglio, Nanotechnology 21, 274007 (2010)10.1088/0957-4484/21/27/274007) we developed the atomic approach by considering only one variational parameter that is used to adjust the correct height of the Kondo peak by imposing the satisfaction of the Friedel sum rule. To obtain the correct width of the Kondo peak in the present work, we consider an additional variational parameter that guarantees this quantity. The two constraints now imposed on the formalism are the satisfaction of the Friedel sum rule and the correct Kondo temperature. In the first part of the work, we present a general derivation of the method for the single impurity Anderson model (SIAM), and we calculate several density of states representative of the Kondo regime for finite correlation U, including the symmetrical case. In the second part, we apply the method to study the electronic transport through a quantum dot (QD) embedded in a quantum wire (QW), which is realized experimentally by a single electron transistor (SET). We calculate the conductance of the SET and obtain a good agreement with available experimental and theoretical results.

Electronic resonances on a metal surface associated with adsorption

Physical aspects of the nature of chemical bonding of halogenide anions with the surface of a metal electrode during specific adsorption from electrolyte solution were considered on a qualitative level. It was shown that a description of a typical dissipative quantum system (adsorbate-substrate) can be approximated by the one-electron mechanism of bonding, allowing stationary fractional separation of the electron charge density between the atomic core of the anion and metal. Partial charge transfer from anion to metal is due to the tunneling permeability of potential barrier separating the quasi-stationary state of valent electron in the anion from free electron states in the metal. The local volume density of this charge is formed as a result of potential scattering of electron waves of metal on an anion atomic core and is concentrated near the inner surface in the vicinity of the scattering center. The residual charge of the adsorbed anion is supported by resonant scattering on the atomic core of electron waves of occupied electron states of the metal from the vicinity of the Fermi boundary. Conservation of the total charge is guaranteed by the Friedel sum rule. A physical model was used to interpret the patterns observed in the data of electrosorption valency measurements.

Dephasing by a Zero-Temperature Detector and the Friedel Sum Rule

Detecting the passage of an interfering particle through one of the interferometer's arms, known as "which path" measurement, gives rise to interference visibility degradation (dephasing). Here, we consider a detector at equilibrium. At finite temperature, dephasing is caused by thermal fluctuations of the detector. More interestingly, in the zero-temperature limit, equilibrium quantum fluctuations of the detector give rise to dephasing of the out-of-equilibrium interferometer. This dephasing is a manifestation of an orthogonality catastrophe, which differs qualitatively from Anderson's. Its magnitude is directly related to the Friedel sum rule.

The Relation between the Electric Conductance of Nanostructure Bridge and Friedel Sum Rule

We analyze the electric conductance through nanostructure bridges in terms of phase-shifts, which satisfy the Friedel sum rule. The phase-shifts are given by solving the eigenvalue equation obtained by extending the method applied to a single impurity problem in a metal. The local charge neutrality condition is introduced through the Friedel sum rule. It is analytically shown that the electric conductance can increase as the two electrodes separate with the condition in which the phase-shifts satisfy the Friedel sum rule. The increment of the distance between two electrodes is obtained by gradually separating interatomic distance.

Transport calculations based on density functional theory, Friedel's sum rule, and the Kondo effect

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, ${n}_{\mathrm{d}\ensuremath{\sigma}}\ensuremath{\approx}1/2$ for spins $\ensuremath{\sigma}=\ensuremath{\uparrow}\ensuremath{\downarrow}$. Here, the true conductance is strongly suppressed by the Coulomb blockade, while the KS conductance still indicates resonant transport. Conclusions of our analysis are corroborated by DFT studies with numerically exact exchange-correlation functionals reconstructed from calculations employing the density matrix renormalization group.

Numerical study of Kondo impurity models with strong potential scattering: Reverse Kondo effect and antiresonance

Accurate numerical results are derived for transport properties of Kondo impurity systems with potential scattering and orbital degeneracy. Using the continuous-time quantum Monte Carlo (CT-QMC) method, static and dynamic physical quantities are derived in a wide temperature range across the Kondo temperature T_K. With strong potential scattering, the resistivity tends to decrease with decreasing temperature, in contrast to the ordinary Kondo effect. Correspondingly, the quasi-particle density of states obtains the antiresonance around the Fermi level. Thermopower also shows characteristic deviation from the standard Kondo behavior, while magnetic susceptibility follows the universal temperature dependence even with strong potential scattering. It is found that the t-matrix in the presence of potential scattering is not a relevant quantity for the Friedel sum rule, for which a proper limit of the f-electron Green's function is introduced. The optical theorem is also discussed in the context of Kondo impurity models with potential scattering. It is shown that optical theorem holds not only in the Fermi-liquid range but also for large energies, and therefore is less restrictive than the Friedel sum rule.

Temperature dependence of scattering phases and Friedel phase discontinuity in quantum wires

Two important issues concerning the scattering phases in a quantum wire with an attractive scatterer are investigated. We consider the case of two quasibound states which couple to a scattering channel and give rise to two Fano resonances. First, we examine the effects of temperature on the phase of the transmission amplitude and the Friedel phase. It is shown that temperature effects tend to smear sharp features of the transmission phase; namely, the phase drops become less than π, and acquire finite widths which increase linearly in the low-temperature regime. The influence of temperature on the Friedel phase and density of states becomes stronger as the Fano resonance becomes narrower. Second, we examine the behavior of the Friedel phase when the energy of the incident electron crosses an infinitely narrow Fano resonance, forming bound state in the continuum. It is shown that the Friedel phase exhibits abrupt jump of π at this energy. We discuss this odd behavior in relation to the Friedel sum rule and point out its consequences on the charge in the scattering region.

RKKY interaction and the nature of the ground state of double dots in parallel

We argue through a combination of slave-boson mean-field theory and the Bethe ansatz that the ground state of closely spaced double quantum dots in parallel coupled to a single effective channel are Fermi liquids. We do so by studying the dots' conductance, impurity entropy, and spin correlation. In particular, we find that the zero-temperature conductance is characterized by the Friedel sum rule, a hallmark of Fermi-liquid physics, and that the impurity entropy vanishes in the limit of zero temperature, indicating that the ground state is a singlet. This conclusion is in opposition to a number of numerical renormalization-group studies. We suggest a possible reason for the discrepancy.

First-principles calculation of transition-metal impurities in LaFeAsO

We present a systematic ab initio study based on density-functional calculations to understand impurity effects in iron-based superconductors. Effective tight-binding Hamiltonians for the d-bands of LaFeAsO with various transition-metal impurities such as Mn, Co, Ni, Zn, and Ru are constructed using maximally-localized Wannier orbitals. Local electronic structures around the impurity are quantitatively characterized by their onsite potential and transfer hoppings to neighboring sites. We found that the impurities are classified into three groups according to the derived parameters: For Mn, Co, and Ni, their impurity-3d levels measured from the Fe-3d level are nearly 0.3 eV, -0.3 eV, and -0.8 eV, respectively, while, for the Zn case, the d level is considerably deep as -8 eV. For the Ru case, although the onsite-level difference is much smaller as O(0.1) eV, the transfer integrals around the impurity site are larger than those of the pure system by 20% \sim 30%, due to the large spatial spread of the Ru-4d orbitals. We also show that, while excess carriers are tightly trapped around the impurity site (due to the Friedel sum rule), there is a rigid shift of band structure near the Fermi level, which has the same effect as carrier doping.

Theoretical study of electric conductance of atomic contact with the Friedel sum rule

We analyze the electric conductance through nanostructure bridges in terms of phase-shifts, which satisfy the Friedel sum rule. The phase-shifts are given by solving the eigenvalue equation obtained by extending the method applied to a single impurity problem in a metal. We introduce the charge neutrality condition through the Friedel sum rule. It is analytically shown that the electric conductance is quantized and can increase as the two electrodes separate under the condition in which the phase-shifts satisfy the Friedel sum rule.