Kondo impurities in nanoscopic and mesoscopic systems

We present results for Kondo impurities in nanoscopic systems. Using Wilson's numerical renormalization group we analyze two different situations: an isolated system with a discrete spectrum of well-defined energy levels and a fixed number of electrons and a nanoscopic system weakly coupled to a macroscopic reservoir. In the latter case, new regimes not observed in macroscopic homogeneous systems are induced by the confinement of conduction electrons. These new confinement-induced regimes are very different depending on whether the Fermi energy is at resonance or between two quasi-bound states.     

Spin filters with Fano dots

We compute the zero bias conductance of electrons through a single ballistic channel weakly coupled to a side quantum dot with Coulomb interaction. In contrast to the standard setup which is designed to measure the transport through the dot, the channel conductance reveals Coulomb blockade dips rather then peaks due to the Fano-like backscattering. At zero temperature the Kondo effect leads to the formation of broad valleys of small conductance corresponding to an odd number of electrons on the dot. By applying a magnetic field in the dot region we find two dips corresponding to a total suppression in the conductance of spins up and down separated by an energy of the order of the Coulomb interaction. This provides a possibility of a perfect spin filter.Received: 6 November 2003, Published online: 2 April 2004PACS: 72.15.Qm Scattering mechanisms and Kondo effect - 73.23.Ad Ballistic transport - 72.25.-b Spin polarized transport     

Some comments on Kondo lattices and the Mott transition

The so called exhaustion problem occurs when few electrons have to screen many spins in a metal with magnetic impurities. A singlet Fermi liquid ground state is possible only if all impurities are “isotropized” in such a way as to suppress their entropy. That takes a time and the corresponding energy limits the Fermi liquid range. The present note explores that issue of time and energy scales, and it concludes that is much smaller than the single impurity Kondo temperature. Similarly the relevant energy scale is proportional to the number of electrons. Recent results on the Mott metal insulator transition in infinite dimension are reconsidered in the light of these results: controversies in that respect are shown to reduce to a simple physical question, with no firm answer as to now. Received: 5 May 1998 / Received in final form and Accepted: 29 July 1998     

Temperature dependence of a single Kondo impurity

Recent advances in scanning tunneling microscopy have allowed the observation of the Kondo effect for individual magnetic atoms. One hallmark of the Kondo effect is a strong temperature-induced broadening of the Kondo resonance. In order to test this prediction for individual impurities, we have investigated the temperature dependent electronic structure of isolated Ti atoms on Ag(100). We find that the Kondo resonance is strongly broadened in the temperature range T = 6.8 K to T = 49.0 K. These results are in good agreement with theoretical predictions for Kondo impurities in the Fermi liquid regime, and confirm the role of electron-electron scattering as the main thermal broadening mechanism.     

The anisotropic multichannel spin-$\mathsf{S}$ Kondo model: Calculation of scales from a novel exact solution

A novel exact solution of the multichannel spin-S Kondo model is presented, based on a lattice path integral approach of the single channel spin-1/2 case. The spin exchange between the localized moment and the host is of XXZ-type, including the isotropic XXX limit. The free energy is given by a finite set of non-linear integral equations, which allow for an accurate determination of high- and low-temperature scales.Received: 9 June 2004, Published online: 3 August 2004PACS: 72.15.Qm Scattering mechanisms and Kondo effect - 04.20.Jb Exact solutions - 75.20.Hr Local moment in compounds and alloys; Kondo effect, valence fluctuations, heavy fermions - 75.10.Lp Band and itinerant models     

Quantum entanglement in elliptical quantum corrals

Quantum corrals present interesting properties due to the combination of confinement and, in the case of elliptical corrals, to their focalizing properties. We study the case when two magnetic impurities are added to the non-interacting corral, where they interact via a superexchange AF interaction J with the surface electrons in the ellipse. Previous results showed that, when both impurities are located at the foci of the system, they experience an enhanced magnetic interaction, as compared to the one they would have in an open surface. For small J and even filling, they are locked in a singlet state, which weakens for larger values of this parameter. When J is much larger than the hopping parameter of the electrons in the ellipse, both spins decorrelate while forming a local singlet with the electrons of the ellipse, thus presenting a confined RKKY–Kondo transition.We interpret this behaviour by means of the von Neumann entropy between the localized impurities and the itinerant electrons of the ellipse: for small J the entropy is nearly zero while for large J it is maximum. In addition, the local density of states provides us with a concrete experimental tool for detecting the Kondo regime.     

Mapping itinerant electrons around Kondo impurities

We investigate single Fe and Co atoms buried below a Cu(100) surface using low temperature scanning tunneling spectroscopy. By mapping the local density of states of the itinerant electrons at the surface, the Kondo resonance near the Fermi energy is analyzed. Probing bulk impurities in this well-defined scattering geometry allows separating the physics of the Kondo system and the measuring process. The line shape of the Kondo signature shows an oscillatory behavior as a function of depth of the impurity as well as a function of lateral distance. The oscillation period along the different directions reveals that the spectral function of the itinerant electrons is anisotropic.     

Charge Kondo anomalies in PbTe doped with Tl impurities

We investigate the properties of PbTe doped with a small concentration x of Tl impurities acting as acceptors and described by Anderson impurities with negative onsite correlation energy. We use the numerical renormalization group method to show that the resulting charge Kondo effect naturally accounts for the unusual low temperature and doping dependence of normal state properties, including the self-compensation effect in the carrier density and the nonmagnetic Kondo anomaly in the resistivity. These are found to be in good qualitative agreement with experiment. Our results for the Tl s-electron spectral function provide a new interpretation of point contact data.     

Molecular Kondo resonance in atomic Fermi gases

The usual Kondo effect is associated with the formation of a many-body ground state that contains a quantum-mechanical entanglement between a (localized) fermion and the free fermions. We show, however, that also a bosonic form of the Kondo effect can occur in degenerate atomic Fermi gases near a Feshbach resonance, if the energy of the diatomic molecular level associated with the Feshbach resonance approaches twice the Fermi energy of the atoms.     

Ruderman-Kittel-Kasuya-Yosida and magnetic-field interactions in coupled Kondo quantum dots

We investigate theoretically the transport properties of two independent artificial Kondo impurities. They are coupled together via a tunable Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction. For strong enough antiferromagnetic RKKY interaction, the impurity density of states increases with the applied in-plane magnetic-field. This effect can be used to distinguish between antiferromagnetic and ferromagnetic RKKY interactions. These results may be relevant to explain some features of recent experiments by Craig et al. [Science 304, 565 (2004)].     

Dynamic transport characteristics of side-coupled double-quantum-impurity systems

A systematic study is performed on time-dependent dynamic transport characteristics of a side-coupled double-quantum-impurity system based on the hierarchical equations of motion. It is found that the transport current behaves like a single quantum dot when the coupling strength is low during tunneling or Coulomb coupling. For the case of only tunneling transition, the dynamic current oscillates due to the temporal coherence of the electron tunneling device. The oscillation frequency of the transport current is related to the step voltage applied by the lead, while temperature $T$, electron--electron interaction $U$ and the bandwidth $W$ have little influence. The amplitude of the current oscillation exists in positive correlation with $W$ and negative correlation with $U$. With the increase in coupling $t_{12}$ between impurities, the ground state of the system changes from a Kondo singlet of one impurity to a spin singlet of two impurities. Moreover, lowering the temperature could promote the Kondo effect to intensify the oscillation of the dynamic current. When only the Coulomb transition is coupled, it is found that the two split-off Hubbard peaks move upward and have different interference effects on the Kondo peak at the Fermi surface with the increase in $U_{12}$, from the dynamics point of view.     

Nonperturbative scaling theory of free magnetic moment phases in disordered metals

The crossover between a free magnetic moment phase and a Kondo phase in low-dimensional disordered metals with dilute magnetic impurities is studied. We perform a finite-size scaling analysis of the distribution of the Kondo temperature obtained from a numerical renormalization group calculation of the local magnetic susceptibility for a fixed disorder realization and from the solution of the self-consistent Nagaoka-Suhl equation. We find a sizable fraction of free (unscreened) magnetic moments when the exchange coupling falls below a critical value Jc. Between the free moment phase due to Anderson localization and the Kondo-screened phase we find a phase where free moments occur due to the appearance of random local pseudogaps at the Fermi energy whose width and power scale with the elastic scattering rate 1/tau.     

Conductance of metallic nanoribbons with defects

The conductances of two typical metallic graphene nanoribbons with one and two defects are studied using the tight binding model with the surface Green’s function method. The weak scattering impurities, U ～ 1 eV, induce a dip in the conductance near the Fermi energy for the narrow zigzag graphene nanoribbons. As the impurity scattering strength increases, the conductance behavior at the Fermi energy becomes more complicated and depends on the impurity location, the AA and AB sites. The impurity effect then becomes weak and vanishes with the increase in the width of the zigzag graphene nanoribbons (150 nm). For the narrow armchair graphene nanoribbons, the conductance at the Fermi energy is suppressed by the impurities and becomes zero with the increase in impurity scattering strength, U > 100 eV, for two impurities at the AA sites, but becomes constant for the two impurities at the AB sites. As the width of the graphene nanoribbons increases, the impurity effect on the conductance at the Fermi energy depends sensitively on the vacancy location at the AA or AB sites.     

The formation of heavy-fermion states in non-Fermi-liquid impurity systems

A mechanism for the occurrence of heavy-fermion states in non-Fermi-liquid (NFL) metals with f-shell impurities is proposed. The impurity with an unstable valence is suggested to have an energy spectrum consisting of a deep f-level and quasicontinuum states (narrow band) in resonance with the Fermi energy. Depending on the impurity concentration, the single-site NFL states are generated by the two-channel Kondo scattering for the low concentration (the Kondo regime) or by the screening interaction for a relatively high concentration (the X-ray-edge regime). It is shown that the NFL states are unstable against the scattering of the NFL excitations by electron states of the narrow band. This scattering generates additional narrow Fermi-liquid (FL) resonances at/near the Fermi level in the Kondo regime and in the X-ray-edge regime. The mixed-valence states are shown to be induced by new FL resonances. The mixed valence mechanism is local and is related to the instability of single-site NFL states. The FL resonances lead to the existence of additional energy scales and of pseudogaps near the Fermi level in the mixed-valence states. They also considerably narrow the region with a nearly integer valence.     

Out-of-equilibrium Kondo effect in a mesoscopic device

We study the nonequilibrium regime of the Kondo effect in a quantum dot laterally coupled to a narrow wire. We observe a split Kondo resonance when a finite bias voltage is imposed across the wire. The splitting is attributed to the creation of a double-step Fermi distribution function in the wire. Kondo correlations are strongly suppressed when the voltage across the wire exceeds the Kondo temperature. A perpendicular magnetic field enables us to selectively control the coupling between the dot and the two Fermi seas in the wire. Already at fields of order 0.1 T only the Kondo resonance associated with the strongly coupled reservoir survives.     

Kondo晶格中的超导理论

为解释重费密子超导现象,本文在Kondo晶格中建立了S波和P波超导理论,并在推广的Nambu空间中对f电子和传导电子的杂化作用进行了自洽处理,计算了有关物理量。理论证明:如果认为f电子参与超导,对S波,所得到的超导转变温度与Tachiki等人的结果一致,但比热跃交与他们的不同,本文的结果更合理些;对P波,由Kondo晶格模型描述的重费密子超导系统等效于修正的局域的费密超流体。此外,本文还研究了杂质散射对超导态的影响,并对各种不同的超导态分别得到了出现无能隙超导的条件。 关键词：     

Fano--Kondo Effect in a Triple Quantum Dots Coupled to Ferromagnetic Leads

Using the Keldysh nonequilibrium Green function and equation-of-motion technique, we have qualitatively studied the spin-dependent transport of a triple-QD system in the Kondo regime. It is shown that the Kondo resonance and Fang interference coexist, and in this system the Fang Kondo effect shows dip behaviours richer than that in the T-shaped QDs. The interdot coupling, the energy level of the side coupled QDs and the spin polarization strength greatly influence the DOS of the central quantum dot QDo. Either the increase of the coupling strength between the two QDs or that of the energy levels of the side coupled QDs enhances the Kondo resonance. Especially, the Kondo resonance is strengthened greatly when the side dot energy is fixed at the Fermi energy. Meanwhile, the Kondo resonance splits for the spin-up and spin-down configurations due to the polarization： the down-spin resonance is enhanced, and the up-spin resonance is suppressed.     

Kondo effect in side coupled double quantum-dot molecule

Electron tunneling through a double quantum-dot molecule side attached to a quantum wire, in the Kondo regime, is studied. The mean-field finite-U slave-boson formalism is used to obtain the solution of the problem. We found conductance cancellations when the molecular energies of the side attached double quantum-dot cross the Fermi energy. We investigate the many body molecular Kondo states and its interplay with the inter-dot antiferromagnetic correlation as a function of the parameters of the system.     

Enhanced superconductivity by correlations between two Kondo impurities

We study the interplay between magnetic correlations of two Kondo impurities and superconducting singlet pairing. Performing a Schrieffer-Wolff transformation in the zero-bandwidth limit of the two-impurity Anderson model we obtain the Hamiltonian of two magnetic impurities and we add a superconducting term to the conduction electrons. The model allows us to study the effect of the magnetic correlation between the impurities on the superconducting ground state. At zero temperature, different superconducting ground states can be obtained depending on the magnitude of magnetic coupling between S₁ and S₂. For increasing coupling, the superconducting region is enlarged showing an interesting result: in the strong coupling limit, where the impurities are in a very strong ferromagnetic correlation state, half of the conduction electrons are decoupled from the local moments of the impurities and take advantage of the superconducting pairing lowering the ground state energy. On the contrary, when the coupling between S₁and S₂ decreases, the scenario of the two independent Kondo impurities in presence of superconductivity emerges and all the conduction electrons are involved in the pair breaking physics. At finite temperature, we obtain the phase diagram and we observe a region of parameters where the re-entrance phenomenon occurs.