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.     

Enhancement of the Kondo effect through Rashba spin-orbit interactions

We study a one-orbital Anderson impurity in a two-dimensional electron bath with Rashba spin-orbit interactions in the Kondo regime. The spin SU(2) symmetry-breaking term couples the impurity to a two-band electron gas. A Schrieffer-Wolff transformation shows the existence of the Dzyaloshinsky-Moriya interaction away from the particle-hole symmetric impurity state. A renormalization group analysis reveals a two-channel Kondo model with ferro- and antiferromagnetic couplings. The parity-breaking Dzyaloshinsky-Moriya term renormalizes the antiferromagnetic Kondo coupling with an exponential enhancement of the Kondo temperature.     

One- and two-channel Kondo model with logarithmic Van Hove singularity: A numerical renormalization group solution

Simple scaling consideration and NRG solution of the one- and two-channel Kondo model in the presence of a logarithmic Van Hove singularity at the Fermi level is given. The temperature dependences of local and impurity magnetic susceptibility and impurity entropy are calculated. The low-temperature behavior of the impurity susceptibility and impurity entropy turns out to be non-universal in the Kondo sense and independent of the s–d coupling J. The resonant level model solution in the strong coupling regime confirms the NRG results. In the two-channel case the local susceptibility demonstrates a non-Fermi-liquid power-law behavior.     

Two energy scales and slow crossover in YbAl3

Experimental results for the susceptibility, magnetization, specific heat, 4f occupation number, Hall effect, and magnetoresistance for single crystals of the intermediate valence (IV) compound YbAl3 show that, in addition to the Kondo temperature scale T(K) approximately 670 K, there is a low temperature scale T(coh) approximately 30-40 K for the onset of Fermi liquid coherence. Furthermore, the crossover from the low temperature Fermi liquid regime to the high temperature local moment regime is slower than predicted by the Anderson impurity model. We suggest that these effects are generic for IV compounds and we discuss them in terms of the theory of the Anderson lattice.     

Composite spin-triplet superconductivity in an symmetric lattice model

The two-channel Anderson lattice model which has SU (2) ⊗ SU (2) symmetry is of relevance to understanding of the magnetic, quadrupolar and superconducting phases in U_1-xTh_xBe₁₃ or Pr based skutterudite compounds such as PrFe₄P₁₂ or PrOs₄Sb₁₂. Possible unconventional superconducting phases of the model are explored. They are characterized by a composite order parameter comprising of a local magnetic or quadrupolar moment and a triplet conduction electron Cooper-pair. This binding of local degrees of freedom removes the entropy of the non Fermi-liquid normal state. We find superconducting transitions in the intermediate valence regime which are suppressed in the stable moment regime. The gap function is non analytic and odd in frequency: a pseudo-gap develops in the conduction electron density of states which vanishes as |ω| close to ω = 0. In the strong intermediate valent regime, the gap function acquires an additional -dependence. Received 28 February 2002 / Received in final form 18 April 2002 Published online 9 July 2002     

Exotic Kondo effects in metals: Magnetic ions in a crystalline electric field and tunnelling centres

The ordinary single-channel Kondo model consists of one or more spin-½ local moments interacting antiferromagnetically with conduction electrons in a metal. This model has provided a paradigm for understanding many phenomena of strongly correlated electronic materials, ranging from the formation of heavyfermion Fermi liquids to the mapping of a one-band model in the cuprate superconductors. The simplest extension of this ordinary Kondo model in metals which yields exotic non-Fermi-liquid physics is the multichannel Kondo impurity model in which the conduction electrons are given an extra quantum label known as the channel or flavour index. In the overcompensated regime of this model, nonFermi-liquid physics is possible, in contrast with the single-channel model. We overview here the multichannel Kondo impurity model candidates most extensively studied for explaining real materials, specifically the two-level system Kondo model relevant for metallic glasses, nanoscale devices and some doped semiconductors, and the quadrupolar and magnetic two-channel Kondo models developed for rare-earth and actinide ions with crystal-field splittings in metals. We provide an extensive justification for the derivation of the theoretical models, noting that, whenever the local impurity degree of freedom is non-magnetic, a two-channel Kondo model must follow by virtue of the magnetic spin degeneracy of the conduction electrons. We carefully delineate all energy and symmetry restrictions on the applicability of these models. We describe the various methods used to study these models along with their results and limitations (multiplicative renormalization group, numerical renormalization group, non-crossing approximation, conformal field theory and Abelian bosonization), all of which provide differing and useful views of the physics. We pay particular attention to the role that scale invariance plays in all these theoretical approaches. We point out in each case how various perturbing fields (magnetic, crystalline electric, electric field gradients and uniaxial stress) may destabilize the non-Fermi-liquid fixed point. We then provide an extensive discussion of the experimental evidence for the relevance of the two-level system Kondo model to metallic glasses and nanoscale devices, and of the quadrupolar and magnetic two-channel models to a number of heavyfermion-based alloys and compounds. We close with a discussion of the extension of the single-impurity models which comprise the main focus of this review to other systems (Coulomb blockade), multiple impurities and lattice models. In the latter case, we provide an overview of the relevance of the two-channel Kondo lattice model to non-Fermi-liquid behaviour and exotic superconductivity in heavy-fermion compounds and to the theoretical possibility of odd-frequency superconductivity, which is realized (for the first time) in the limit of infinite spatial dimensions for this model.     

Photoemission spectroscopy of magnetic and nonmagnetic impurities on the surface of the Bi2Se3 topological insulator

Dirac-like surface states on surfaces of topological insulators have a chiral spin structure that suppresses backscattering and protects the coherence of these states in the presence of nonmagnetic scatterers. In contrast, magnetic scatterers should open the backscattering channel via the spin-flip processes and degrade the state's coherence. We present angle-resolved photoemission spectroscopy studies of the electronic structure and the scattering rates upon the adsorption of various magnetic and nonmagnetic impurities on the surface of Bi2Se3, a model topological insulator. We reveal a remarkable insensitivity of the topological surface state to both nonmagnetic and magnetic impurities in the low impurity concentration regime. Scattering channels open up with the emergence of hexagonal warping in the high-doping regime, irrespective of the impurity's magnetic moment.     

Phase diagram of an impurity in the spin-1/2 chain: two-channel Kondo effect versus Curie law

We consider a magnetic S = 1/2 impurity in the antiferromagnetic spin chain as a function of two coupling parameters: the symmetric coupling of the impurity to two sites in the chain J1 and the coupling between the two sites J2. By using field theory arguments and numerical calculations we can identify all possible fixed points and classify the renormalization flow between them, which leads to a nontrivial phase diagram. Depending on the detailed choice of the two (frustrating) coupling strengths, the stable phases correspond either to a decoupled spin with Curie law behavior or to a non-Fermi-liquid fixed point with a logarithmically diverging impurity susceptibility as in the two-channel Kondo effect. Our results resolve a controversy about the renormalization flow.     

Mapping of the anisotropic two-channel Anderson model onto a Fermi-Majorana biresonant level model

We establish the correspondence between an extended version of the two-channel Anderson model and a particular type of biresonant level model. For certain values of the parameters the new model becomes quadratic. We calculate in closed form the entropy and impurity occupation as functions of temperature and identify the different physical energy scales of the problem. We show how, as the temperature goes to zero, the model approaches a universal line of fixed points non-Fermi liquid in nature.     

Magnetoresistance of mixed valent Tm impurities

The resistivity of a metal due to an Anderson impurity with orbital degeneracy in the intermediate valence regime is calculated via the Kubo formula within a mode-mode decoupling scheme. The result depends on the relative occupation of the f-levels and shows a bump as a function of temperature. In the case of Tm the two ionic configurations are magnetic, and a considerable field dependence is obtained.     

Dynamics of a tunneling magnetic impurity: Kondo effect induced incoherence

We study how the formation of the Kondo compensation cloud influences the dynamical properties of a magnetic impurity that tunnels between two positions in a metal. The Kondo effect dynamically generates a strong tunneling impurity-conduction electron coupling, changes the temperature dependence of the tunneling rate, and may ultimately result in the destruction of the coherent motion of the particle at zero temperature. We find an interesting two-channel Kondo fixed point as well for a vanishing overlap between the electronic states that screen the magnetic impurity. We propose experiments where the predicted features could be observed.     

Instability of Non—Fermi Liquid Behavior in the Two—Channel Kondo Model

The effects of interchannel scattering of conduction electrons by the impurity and repulsion of conduction electrons at the impurity site on the two-channel Kondo model are simultaneously considered in this paper,It is shown that these two perturbations will substantially modify the usual local non-Fermi liquid behavior of the two-channel Kondo model.With bosonization and unitary transformations we find that the system can be transformed into a single channel Kondo model with anisotropy between longitudinal and transverse exchange couplings,Whatever for originally antiferromagnetic or ferromagnetic isotropic coupling,the system always flows to strong-coupling limit,which exhibits local Fermi liquid behavior at low temperatures.     

Pressure-induced valence crossover in superconducting CeCu2Si2

Measurement of the Ce valence in the heavy fermion CeCu(2)Si(2) is reported for the first time under pressure and at low temperature (T=14 K) in proximity of the superconducting region. CeCu(2)Si(2) is considered as a strong candidate for a new type of pairing mechanism related to critical valence fluctuations which could set in at high pressure in the vicinity of the second superconducting dome. A quantitative estimate of the valence in this pressure region was achieved from the measurements of the Ce L(3) edge in the high-resolution partial-fluorescence yield mode and subsequent analysis of the spectra within the Anderson impurity model. While a clear increase of the Ce valence is found, the weak electron transfer and the continuous valence change under pressure suggests a crossover regime with the hypothetical valence line terminating at a critical end point T(cr) close to zero.     

Microscopic analysis of the valence band and impurity band theories of (Ga,Mn)As

We analyze microscopically the valence and impurity band models of ferromagnetic (Ga,Mn)As. We find that the tight-binding Anderson approach with conventional parametrization and the full potential local-density approximation+U calculations give a very similar band structure whose microscopic spectral character is consistent with the physical premise of the k·p kinetic-exchange model. On the other hand, the various models with a band structure comprising an impurity band detached from the valence band assume mutually incompatible microscopic spectral character. By adapting the tight-binding Anderson calculations individually to each of the impurity band pictures in the single Mn impurity limit and then by exploring the entire doping range, we find that a detached impurity band does not persist in any of these models in ferromagnetic (Ga,Mn)As.     

Nernst constant of the doped cuprate in the ‘normal’ state: A scaling form

A first analytic calculation has been done in Nernst constant on the basis of the hypothesis that the normal state of the underdoped cuprate is at the two-channel Kondo fixed point of the crystal. Its temperature variation is found to obey a universal scaling relation, which can be checked experimentally. It has the maximum in the pseudogap regime, which has been already found experimentally. We present argument and evidence that in the doped and moderately disordered cuprate the two-channel fixed point is stable.     

Polarization of valence band holes in the (Ga,Mn)as diluted magnetic semiconductor

We report on direct measurements of the impurity band hole polarization in the diluted magnetic semiconductor (Ga,Mn)As. The polarization of impurity band holes in a magnetic field is strongly enhanced by antiferromagnetic exchange interaction with Mn ions. The temperature dependence of the hole polarization shows a strong increase of this polarization below the Curie temperature. We show that the ground state of the impurity band is formed by uniaxial stress split F=+/-1 states of antiferromagnetically coupled Mn ions (S=5/2) and valence band holes (J=3/2). The gap between the Mn acceptor related impurity band and the valence band is directly measured in a wide range of Mn content.     

Non-universal Fermi polaron in quasi two-dimensional quantum gases

We consider an impurity problem in a quasi-two-dimensional Fermi gas, where a spin-down impurity is immersed in a Fermi sea of N spin-up atoms. Using a variational approach and an effective two-channel model, we obtain the energy for a wide range of interaction strength and for various different mass ratios between the impurity and the background fermion in the context of heteronuclear mixture. We demonstrate that in a quasi-two-dimensional Fermi gas there exists a transition of the ground state from polaron in the weakly interacting region to molecule in the strongly interacting region. The critical interaction strength of the polaron-molecule transition is non-universal and depends on the particle density of the background Fermi sea. We also investigate the excited repulsive polaron state, and find similar non-universal behavior.     

Variational local moment approach: From Kondo effect to Mott transition in correlated electron systems

The variational local moment approach (VLMA) solution of the single impurity Anderson model is presented. It generalizes the local moment approach of Logan et al. by invoking the variational principle to determine the lengths of local moments and orbital occupancies. We show that VLMA is a comprehensive, conserving and thermodynamically consistent approximation and treats both Fermi and non-Fermi liquid regimes as well as local moment phases on equal footing. We tested VLMA on selected problems. We solved the single- and multi-orbital impurity Anderson model in various regions of parameters, where different types of Kondo effects occur. The application of VLMA as an impurity solver of the dynamical mean-field theory, used to solve the multi-orbital Hubbard model, is also addressed.     

Theory of quasimagnetic impurity in a metal: An exactly soluble model of interacting electrons

We study an impurity atom, on which two-body forces are important, dissolved in a metal, where they are negligible. With the aid of the well-known boson excitation spectrum of the electronic Fermi sea, we predict the low-energy effects of one- and two-body potentials on the impurity, in the nonmagnetic regime. We obtain for the first time exact expressions for the cutoff independent contributions to the specific heat and paramagnetic susceptibility, the spectral amplitudes or one-electron density of states on the impurity, and the scattering cross-section. The entire spectrum of manybody eigenstates is explicitly obtained. The onset of a local magnetic moment appears as a sudden breakdown of the model Hamiltonian, and occurs when the two-body potential exceeds a critical value U_c which is O(E_F) in magnitude. A study of the renormalization of the interaction parameters terminates the paper.