Fermi-liquid theory for the single-impurity Anderson model (original) (raw)
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Conductances in the Two-Impurity Anderson Model
In a number of systems of interest that involve magnetic atoms and their analogous quantum dot manifestations, there arises a competition between Kondo screening and various types of magnetic ordering (direct and induced). This competition can be studied in detail using scanning tunneling microscopy to probe clusters of magnetic adatoms on metallic surfaces and has direct implications for systems of double quantum dots. In both of these cases, an observable quantity of interest is the electrical conductance, which can be calculated by applying the numerical renormalization group to the two-impurity Anderson model. Depending on their separation and the strength of their exchange interaction, pairs of magnetic adatoms may exhibit ferromagnetic or antiferromagnetic alignment of the impurity local moments, in some cases leading to a two-stage Kondo screening process, effectively isolated impurity screening, or a complete suppression of the Kondo effect. These behaviors have different signatures in the differential conductance. A class of double quantum dot devices composed of a Kondo-like dot and a weakly interacting dot is predicted to display a splitting of the Kondo resonance and a pair of quantum phase transitions. These behaviors introduce unique signatures in the device conductance when the level energy on either dot is varied by tuning the appropriate gate voltage. This work demonstrates that double quantum dots can provide a controlled experimental setting in which to study quantum phase transitions in a strongly correlated system.
Conductance of a spin-1 quantum dot: The two-stage Kondo effect
Physical Review B, 2007
We discuss the physics of a of a spin-1 quantum dot, coupled to two metallic leads and develop a simple model for the temperature dependence of its conductance. Such quantum dots are described by a two-channel Kondo model with asymmetric coupling constants and the spin screening of the dot by the leads is expected to proceed via a two-stage process. When the Kondo temperatures of each channel are widely separated, on cooling, the dot passes through a broad cross-over regime dominated by underscreened Kondo physics. A singular, or non-fermi liquid correction to the conductance develops in this regime. At the lowest temperatures, destructive interference between resonant scattering in both channels leads to the eventual suppression of the conductance of the dot. We develop a model to describe the growth, and ultimate suppression of the conductance in the two channel Kondo model as it is screened successively by its two channels. Our model is based upon large-N approximation in which the localized spin degrees of freedom are described using the Schwinger boson formalism.
Physical Review B, 2008
The eigenstates of an isolated nanostructure may get mixed by the coupling to external leads. This effect is the stronger, the smaller the level splitting on the dot and the larger the broadening induced by the coupling to the leads is. We describe how to calculate the nondiagonal density matrix of the nanostructure efficiently in the cotunneling regime. As an example we consider a system of two quantum dots in the Kondo regime, the two spins coupled by an antiferromagnetic exchange interaction and each dot tunnel-coupled to two leads. Calculating the nonequilibrium density matrix and the corresponding current, we demonstrate the importance of the off-diagonal terms in the presence of an applied magnetic field and a finite bias-voltage.
Theory of the non-Fermi-liquid transition point in the two-impurity Kondo model
Physical review. B, Condensed matter, 1993
We present an explicit solution of the problem of two coupled spin-impurities, interacting with a band of conduction electrons. We obtain an exact e6'ective bosonized Hamiltonian, which is then treated by two different methods (low-energy theory and mean-field approach). Scale invariance is explicitly shown at the quantum critical point. The staggered susceptibility behaves like ln(T&/T) at low T, whereas the magnetic susceptibility and (S,. sz) are well behaved at the transition. The divergence of C (T) /T when approaching the transition point is also studied. The non-Fermi-liquid (actually marginal-Fermi-liquid) critical point is shown to arise because of the existence of anomalous correlations, which lead to degeneracies between bosonic and fermionic states of the system. The methods developed in this paper are of interest for studying more physically relevant models, for instance, for high-T, cuprates.
Physical Review B
We extend a recently developed Fermi liquid (FL) theory for the asymmetric single-impurity Anderson model [C. Mora et al., Phys. Rev. B 92, 075120 (2015)] to the case of an arbitrary local magnetic field. To describe the system's low-lying quasiparticle excitations for arbitrary values of the bare Hamiltonian's model parameters, we construct an effective low-energy FL Hamiltonian whose FL parameters are expressed in terms of the local level's spin-dependent ground-state occupations and their derivatives with respect to level energy and local magnetic field. These quantities are calculable with excellent accuracy from the Bethe ansatz solution of the Anderson model. Applying this effective model to a quantum dot in a nonequilibrium setting, we obtain exact results for the curvature of the spectral function, c A , describing its leading ∼ ε 2 term, and the transport coefficients c V and c T , describing the leading ∼V 2 and ∼T 2 terms in the nonlinear differential conductance. A sign change in c A or c V is indicative of a change from a local maximum to a local minimum in the spectral function or nonlinear conductance, respectively, as is expected to occur when an increasing magnetic field causes the Kondo resonance to split into two subpeaks. Surprisingly, we find that the fields B A and B V at which c A and c V change sign are parametrically different, with B A of order T K but B V much larger. In fact, in the Kondo limit c V never vanishes, implying that the conductance retains a (very weak) zero-bias maximum even for strong magnetic field and that the two pronounced finite-bias conductance side peaks caused by the Zeeman splitting of the local level do not emerge from zero-bias voltage.
Linear Kondo conductance in a quantum dot
Journal of Physics: Condensed Matter, 2004
In a tunneling experiment across a quantum dot it is possible to change the coupling between the dot and the contacts at will, by properly tuning the transparency of the barriers and the temperature. Gate voltages allow for changes of the relative position of the dot addition energies and the Fermi level of the leads. Here we discuss the two limiting cases: weak and strong coupling in the tunneling Hamiltonian. In the latter case Kondo resonant conductance can emerge at low temperature in a Coulomb blockade valley. We give a pedagogical approach to the single channel Kondo physics at equilibrium and review the Nozières scattering picture of the correlated fixed point. We emphasize the effect of an applied magnetic field and show how an orbital Kondo effect can take place in vertical quantum dots tuned both to an even and an odd number of electrons at a level crossing. We extend the approach to the two channel overscreened Kondo case and discuss recent proposals for detecting the non Fermi Liquid fixed point which could be reached at strong coupling.
Physical Review B, 2005
We investigate the nonequilibrium transport properties of a three-terminal quantum dot in the strongly interacting limit. At low temperatures, a Kondo resonance arises from the antiferromagnetic coupling between the localized electron in the quantum dot and the conduction electrons in source and drain leads. It is known that the local density of states is accessible through the differential conductance measured at the (weakly coupled) third lead. Here, we consider the multiterminal current-current correlations (shot noise and cross correlations measured at two different terminals). We discuss the dependence of the current correlations on a number of external parameters: bias voltage, magnetic field and magnetization of the leads. When the Kondo resonance is split by fixing the voltage bias between two leads, the shot noise shows a nontrivial dependence on the voltage applied to the third lead. We show that the cross correlations of the current are more sensitive than the conductance to the appearance of an external magnetic field. When the leads are ferromagnetic and their magnetizations point along opposite directions, we find a reduction of the cross correlations. Moreover, we report on the effect of dephasing in the Kondo state for a two-terminal geometry when the third lead plays the role of a fictitious voltage probe.
Ground-state of the single impurity Anderson model with correlated conduction electrons
Physics Letters A, 2002
Utilizing the nonperturbative Lanczos procedure, we study the ground-state spectrum of the Single-Impurity Anderson Model. An additional term is added to the Hamiltonian which represents a Coulomb-repulsion between the conduction electrons. The ground-state energy as well as the singlet-triplet energy is calculated in this strongly interacting system. Our results are consistent with those of Fermi-liquid theory which predicts a renormalization of the low energy properties of the system upon introduction of local, repulsive conduction electron interactions.
From the Kondo Regime to the Mixed-Valence Regime in a Single-Electron Transistor
Physical Review Letters, 1998
We demonstrate that the conductance through a single-electron transistor at low temperature is in quantitative agreement with predictions of the equilibrium Anderson model. The Kondo effect is observed when an unpaired electron is localized within the transistor. Tuning the unpaired electron's energy toward the Fermi level in nearby leads produces a crossover between the Kondo and mixedvalence regimes of the Anderson model. [S0031-9007(98)07897-1] PACS numbers: 75.20.Hr, 72.15.Qm, 73.23.Hk The effect of magnetic impurities on metals-the Kondo effect-has been studied for half a century, and enjoys continued relevance today in attempts to understand heavy-fermion materials and high-T c superconductors. Yet it has not been possible to experimentally test the richly varied behavior predicted theoretically. The theory depends on several parameters whose values are not independently tunable for impurities in a metal, and are often not even a priori known. On the other hand, it has been predicted [1-5] that a single-electron transistor (SET) should be described by the Anderson impurity model, and hence should also exhibit the Kondo effect. A SET contains a very small droplet of localized electrons, analogous to an impurity, strongly coupled to conducting leads, analogous to the host metal. We have recently shown that when the number of electrons in the droplet is odd, and hence one electron is unpaired, the SET exhibits the Kondo effect [6] in electronic transport. This observation has since been confirmed with additional quantitative detail. As we show in this Letter, in SET experiments one can tune the important parameters and test predictions of the Anderson model that cannot be tested in bulk metals. We focus here on the equilibrium properties of the model for which the theory is well developed.
Charge Kondo Effect toward a Non-Fermi-Liquid Fixed Point in the Orbitally Degenerate Exchange Model
Journal of the Physical Society of Japan, 1999
We show that a Kondo-type model with an orbital degeneracy has a new non-Fermi-liquid fixed point. Near the fixed point the spin degrees of freedom are completely quenched, and the residual charge degrees of freedom lead to the multi-channel Kondo effect. Anomalous behavior appears in electric and thermal properties, but the magnetic susceptibility should show the local Fermi-liquid behavior. The non-Fermi-liquid fixed point becomes unstable against perturbations breaking the particle-hole symmetry. We derive these results using the third-order scaling for a spherically symmetric model with a fictitious spin. In contrast to the Coqblin-Schrieffer model, the present model respects different time-reversal properties of multipole operators.