Effect of localized spins in coherent transport through quantum dots

The effect of localized spins on the quantum coherence in solids is discussed. A quantum dot with an odd number of electrons can be a model system for a localized spin. It is experimentally shown that a spin flip scattering by a quantum dot pulls the trigger of quantum decoherence. On the other hand, spin flip scattering is the basic process to construct the Kondo singlet state around a magnetic impurity. Through an interference effect of the Kondo state (the Fano–Kondo effect) in a side-coupled dot system, we show experimentally that the Kondo singlet state is quantum mechanically coherent. The analysis of the Fano–Kondo lineshape indicates the locking of the phase shift to π/2, which is in agreement with theoretical predictions. The Fano–Kondo effect is also observed in an Aharonov–Bohm ring, in which a quantum dot is embedded, and also indicates the phase shift locking to π/2.     

On the competition between magnetic order and local Kondo effect in Kondo lattice

We investigate the competition between magnetic order and local Kondo effect in a Kondo lattice model (i.e. the Coqblin-Schrieffer Hamiltonian extended to a lattice) in a mean-field approximation, taking account of the spin-orbit degeneracy of each localized f level. This leads to the definition of a dependent Kondo temperature. We study the Kondo phase and compare its energy with the energies of magnetic phases, when the number of the conduction band electron per site is near one. We present a phase diagram which shows the occurrence of three phases: Kondo, antiferromagnetic and paramagnetic phases. Our model in the mean-field approximation also shows a somewhat flat Kondo temperature, for large values of , as a function of the exchange coupling J between conduction and localized f electrons. Finally we show some scaling effects between and J and we define a corresponding Kondo temperature. Received 21 September 1998 and Received in final form 8 February 1999     

Spin liquid in an almost ferromagnetic Kondo lattice

A theory of stabilization of a spin liquid in a Kondo lattice at temperatures close to the temperature of antiferromagnetic instability has been developed. Kondo exchange scattering of conduction electrons leads to emergence of a state of the spin liquid of the resonating valence bonds (RVB) type at T>T _K. Owing to this stabilization, low-energy processes of Kondo scattering with energies below T _K are frozen so that the “singlet” state of the Kondo lattice is not realized; instead a strongly correlated spin liquid with developed antiferromagnetic fluctuations occurs. A new version of the Feynman diagram technique has been developed to describe interaction between spin fluctuations and resonant valence bonds in a self-consistent manner. Emergence of a strongly anisotropic RVB spin liquid is discussed. Zh. éksp. Teor. Fiz. 112, 729–759 (August 1997)     

Dynamically induced Kondo effect in double quantum dots

A new mechanism of resonance Kondo tunneling via a composite quantum dot (QD) is proposed. It is shown that, owing to the hidden dynamic spin symmetry, the Kondo effect can be induced by a finite voltage eV applied to the contacts at an even number N of electrons in a QD with zero spin in the ground state. As an example, a double QD is considered in a parallel geometry with N=2, which possesses the SO(4) type symmetry characteristic of a singlet-triplet pair. In this system, the Kondo peak of conductance appears at an eV value compensating for the exchange splitting.     

EPR study of exchange interactions in the nonmagnetic Kondo system La1−x CexCu6

The EPR of paramagnetic impurities Gd³⁺ and Mn²⁺ was studied in nonmagnetic Kondo system La_1−x Ce_xCu₆ containing in the 1.6–200 K range. The exchange interaction parameters of gadolinium and manganese ions with conduction electrons, of cerium ions with conduction electrons and with one another, the Kondo temperature of cerium ions, and the temperature behavior of cerium-ion spin-fluctuation rate have been determined. A pseudogap in the density of states at the Fermi level has been detected in the CeCu₆ regular system, which is apparently due to s-f hybridization. This pseudogap can be destroyed by introducing an aluminum impurity, which induces strong conduction-electron scattering. It was also found that RKKY interaction among manganese ions in CeCu_6−y Mn_y is considerably stronger than it is in LaCu_6−y Mn_y, which implies enhancement of nonlocal spin susceptibility due to an f band contribution to conduction-electron states. Fiz. Tverd. Tela (St. Petersburg) 40, 593–599 (April 1998)     

Breakdown of Luttinger's theorem in two-orbital Mott insulators

An analysis of Luttinger's theorem shows that – contrary to recent claims – it is not valid for a generic Mott insulator. For a two-orbital Hubbard model with two electrons per site the crossover from a non-magnetic correlated insulating phase (Mott or Kondo insulator) to a band insulator is investigated. Mott insulating phases are characterized by poles of the self-energy and corresponding zeros in the Greens functions defining a “Luttinger surface” which is absent for band insulators. Nevertheless, the ground states of such insulators with two electrons per unit cell are adiabatically connected.     

Low temperature Kondo reduction of quadrupolar and magnetic moments in the YbCuAl series

We present measurements in the YbCu_5-xAl_x series, down to the 50 mK range, using ¹⁷⁰Yb M?ssbauer absorption spectroscopy and magnetisation measurements. In this series, the hybridisation between the Yb 4 f electrons and the conduction electrons is known to decrease as the Al content x increases. We apply the variational solution of the impurity Kondo problem to the interpretation of our data. We show that the Kondo temperature can be derived from the measured 4 f quadrupole moment and, for the magnetically ordered compounds (), we obtain the exchange energy as a function of the Al content. Our findings are in general agreement with Doniach's model describing the onset of magnetic ordering according to the relative values of the Kondo and exchange energy scales. Received 16 April 1998     

Crystal field in valence-fluctuating CeNi-based compounds

The effects of the crystal field (CF) on the paramagnetic Pr ion in a number of compounds of the type R_1−x Pr_xNi (R = Ce, La, Y), in which a transition of the cerium ions from an intermediate-valence into a Kondo state occurs as La is substituted for Ce, are investigated. The level schemes of the Pr ion in the CF are reconstructed from inelastic neutron scattering spectra and the temperature dependence of the heat capacity in different magnetic fields (B=0–8 T). The parameters of the low-symmetry CF in the compounds RNi are determined from the experimental data. It is established that in the Kondo regime the hybridization of the f electrons with conduction electrons only gives a proportional increase in all the parameters of the CF potential. At the same time, partial delocalization of the f electrons in the intermediate-valence state results in charge redistribution, which is manifested in different scales for the changes in the different CF parameters. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 12, 947–952 (25 June 1996)     

On the theory of superconductivity in Kondo lattice systems

An attempt is made to explain the occurrence of superconductivity in Kondo lattice systems with special reference to CeCu₂Si₂. Starting point is the Fermi liquid approach. It is generalized from a Kondo impurity to the Kondo lattice by means of the Korringa-Kohn-Rostocker method. From it a hybridization model is derived and discussed in detail. Two electron-phonon mechanisms are investigated which appear in Kondo lattices. One results from the additional phase shifts caused by the Kondo ions while the other is responsible for the so-called Kondo volume collapse. It is shown that the latter is sufficiently strong in order to explain why CeCu₂Si₂ is a superconductor while LaCu₂Si₂ is not. An estimate for the superconducting transition temperatureT _c produces the right order of magnitude.     

Influence of unstable valence of cerium ions on the crystal field in ReNi compounds

To examine the effect of hybridization of 4f electrons with conduction electrons on the crystal field potential using neutron spectroscopy, we studied the effects of the crystal electric field (CEF) in intermetallic compounds of the type ReNi, in which chemical substitution is followed by a transition of the cerium ions from an intermediate valence state to the Kondo state. Measurements were performed both on cerium ions in the compounds Ce_1−x La_xNi (x=0.5, 0.8), where they have a whole-number population of the 4f shell, and on the paramagnetic impurity ion Nd in the series of compounds Re_1−x Nd_xNi (Re=Ce, La, Y), in which the cerium ions are found either in an intermediate valence state or in the Kondo state. From the neutron inelastic magnetic scattering spectra on Nd ions, we have reconstructed the crystal field parameters in ReNi compounds and calculated the CEF level diagram of Ce ions in these compounds as functions of the interion distances Re-Ni. The results of our calculations are in good agreement with the experimentally determined splitting diagram of the ground-state multiplet of the Ce ions. We have determined that as the degree of hybridization with the conduction electrons grows the CEF potential varies considerably and the effective splitting of the 4f shell of the cerium ions increases. The estimated energy scale of the splitting of the ground-state multiplet of the Ce³⁺ ions in the ReNi CEF (Δ_CEF∼15 meV) turns out to be commensurate with the Kondo temperature (T _K ;140 K for CeNi. Analysis indicates that the CEF potential has a substantial effect on the formation of the valence-unstable ground state of the f shell in this compound. Zh. éksp. Teor. Fiz. 113, 1731–1747 (May 1998)     

Quantum crystallization of two-dimensional dipole systems

An analysis is made of the region of existence of crystalline order in a system of spatially separated electrons (e) and holes (h) in two coupled quantum wells for various concentrations n, temperatures T, and distances D between the layers. A study is also made of crystallization in a system of electrons in semiconductor structures near a metal electrode for various distances d between the semiconductor and the metal. Calculations of the crystalline phase were made using variational calculations of the ground-state energy of the system allowing for pairing of quasiparticles with nonzero momentum. For a system of two coupled quantum wells, regions in (T,n,D) space are determined in which electron (or hole) charge-density waves exist in each layer and regions where these charge-density waves are in phase, in other words, indirect excitons (or pairs with spatially separated electrons and holes) interacting as electric dipoles, become crystallized. In the electron system in semiconductor structures near a metal electrode, regions of existence of an electron crystal are also obtained in (T,n,D) space, where over large distances the electrons interact as electric dipoles because of image forces. Fiz. Tverd. Tela (St. Petersburg) 40, 1350–1355 (July 1998)     

Spin glass and antiferromagnetism in Kondo-lattice disordered system

The competition between spin glass (SG), antiferromagnetism (AF) and Kondo effect is studied here in a model which consists of two Kondo sublattices with a Gaussian random interaction between spins in different sublattices with an antiferromagnetic mean J ₀ and standard deviation J. In the present approach there is no hopping of the conduction electrons between the sublattices and only spins in different sublattices can interact. The problem is formulated in the path integral formalism where the spin operators are expressed as bilinear combinations of Grassmann fields which can be solved at mean field level within the static approximation and the replica symmetry ansatz. The obtained phase diagram shows the sequence of phases SG, AF and Kondo state for increasing Kondo coupling. This sequence agrees qualitatively with experimental data of the Ce₂Au_1-x Co _x Si₃ compound.Received: 9 April 2003, Published online: 9 September 2003PACS: 05.50.+q Lattice theory and statistics; Ising problems - 64.60.Cn Order disorder transformations; statistical mechanics of model systems     

Peculiarities of crystal field effects in CeInCu2 based heavy-fermion compounds

We have studied the evolution of the inelastic neutron magnetic scattering spectra of a compound with cubic symmetry, CeInCu₂, in the temperature range 10–130 K, and also their transformation with variation of the Kondo temperature T _K due to substitution of cerium ions in the system Ce_1−x (La,Y)_xInCu₂ at T=10 K. It turns out that the energy of the transition between the ground state and excited state of the 4 f electrons (Δ_CF) in the crystal electric field in CeInCu₂ increases with growth of the population of the ground state as the temperature is reduced, with a slight change in its intensity. Such behavior is inconsistent with the notion of classical one-ion effects of the crystal electric field. We have found that the scale of the observed variations in the excitation spectra of the 4f electrons depends on the Kondo temperature T _K and is insensitive to disorder in the rare-earth sublattice. Thus, despite the fact that T _K ≪Δ_CF, hybridization with states in the conduction band has a substantial effect on all parameters of the excitation spectrum of the ground multiplet of the 4f electrons at low temperatures. Zh. éksp. Teor. Fiz. 115, 2197–2206 (June 1999) A. A. Baikov Institute of Metallurgy     

Drag effects in a two-layer system of spatially separated electrons and excitons

We discuss drag effects in a two-layer system of spatially separated electrons and excitons: the entrainment of excitons by moving electrons, and the entrainment of electrons by moving excitons. For the case of excitons entrained by electrons we find the drag velocity υ _drag, and for electrons entrained by excitons we compute the induced electric field E ₂. These drag effects can be sensitive indicators of the phase state of the excitons and of phase transitions in the exciton system (to a liquid phase, superfluid state, etc.) Zh. éksp. Teor. Fiz. 111, 1107–1119 (March 1997)     

Photoinduced instability and semiconductor-metal phase transition in a Peierls system

A microscopic theory of the appearance of electron-phonon instability and a semiconductor-metal phase transition away from thermodynamic equilibrium in a Peierls system upon the optical excitation of electron-hole pairs is devised. An equation which specifies the dependence of the order parameter of the phase transition and the uniquely related gap width in the electron spectrum, on the concentration n of conduction-band electrons is obtained. The critical concentration n=n _c, above which the semiconductor phase of the system is unstable toward the transition to the metallic state, is calculated. A comparison with an experiment on the irradiation of a substrate-supported vanadium dioxide film by a laser pulse is made. Fiz. Tverd. Tela (St. Petersburg) 40, 2113–2118 (November 1998)     

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.     

Numerical calculation of the fidelity for the Kondo and the Friedel-Anderson impurities

The fidelities of the Kondo and the Friedel-Anderson (FA) impurities are calculated numerically. The ground states of both systems are calculated with the FAIR (Friedel artificially inserted resonance) theory. The ground state in the interacting systems is compared with a nullstate in which the interaction is zero. The different multi-electron states are expressed in terms of Wilson states. The use of N Wilson states simulates the use of a large effective number N _eff of states. A plot of ln(F) versus N ∝ ln(N _eff ) reveals whether one has an Anderson orthogonality catastrophe at zero energy. The results are at first glance surprising. The ln(F) – ln(N _eff ) plot for the Kondo impurity diverges for large N _eff . On the other hand, the corresponding plot for the symmetric FA impurity saturates for large N _eff when the level spacing at the Fermi level is of the order of the singlet-triplet excitation energy. The behavior of the fidelity allows one to determine the phase shift of the electron states in this regime.     

Magnetic order in a Kondo lattice: A neutron scattering study of CeCu2Ge2

Elastic and inelastic neutron scattering studies of the Kondo lattice CeCu₂Ge₂ were performed. AtT _N=4.1 K an incommensurate magnetic order develops with an ordering wave vectorq ₀=(0.28, 0.28, 0.54) and an ordered moment µ _s =0.74 µB. The crystalline electric field splits the 4f ¹-J-multiplet of the Ce ion into a ground state doublet and a quartet at 191 K. The wave function of the ground state yields an ordered moment of 1.54µB. Thus, due to the onset of the formation of a Kondo singlet the magnetic moment is considerably reduced. The magnetic relaxation rate was investigated via quasielastic neutron scattering. The temperature dependence of (T) is characteristic of heavy-fermion systems with a high temperature square root dependence and a limiting low temperature value, yielding a Kondo temperatureT _K10K. The quasielastic component of the scattered neutron intensities persists down to the lowest temperatures, well belowT _N. This quasielastic line is regarded as a characteristic feature of heavy-fermion systems and corresponds to the enhanced value of the linear term of the specific heat.