Distribution Of Kondo Temperatures Research Articles

Multifractality and the distribution of the Kondo temperature at the Anderson transition

Using numerical simulations, we investigate the distribution of Kondo temperatures at the Anderson transition. In agreement with previous work, we find that the distribution has a long tail at small Kondo temperatures. Recently, an approximation for the tail of the distribution was derived analytically. This approximation takes into account the multifractal distribution of the wavefunction amplitudes (in the parabolic approximation), and power law correlations between wave function intensities, at the Anderson transition. It was predicted that the distribution of Kondo temperatures has a power law tail with a universal exponent. Here, we attempt to check that this prediction holds in a numerical simulation of Anderson's model of localisation in three dimensions.

Kondo effect and non-Fermi-liquid behavior in Dirac and Weyl semimetals

We study the Kondo effect in three-dimensional (3D) Dirac materials and Weyl semimetals. We find the scaling of the Kondo temperature with respect to the doping $n$ and the coupling $J$ between the moment of the magnetic impurity and the carriers of the semimetal. We find that when the temperature is much smaller than the Kondo temperature the resistivity due to the Kondo effect scales as the $n^{-4/3}$.We also study the effect of the interplay of long-range scalar disorder and Kondo effect. In the presence of disorder-induced long-range carrier density inhomogeneities the Kondo effect is not characterized by a Kondo temperature but by a distribution of Kondo temperatures. We obtain the expression of such distribution and show that its features cause the appearance of strong non-Fermi liquid behavior. Finally we compare the properties of the Kondo effect in 3D Dirac materials and 2D Dirac systems like graphene and topological insulators.

Distribution of Kondo temperatures in a thin film

The Kondo temperature ${T}_{K}$ and the Kondo exchange energy J are local quantities that are closely related to the density of states. In a thin film, the changes in the density of states near surfaces have strong influence on the values of ${T}_{K}$ and J. In this paper, we present calculations of these quantities for a metallic thin film; we show that they depend on the position of the magnetic impurity in the film and that ${T}_{K}$ and J are distributed through the film.

Kondo impurity band in a one-dimensional correlated electron lattice

We consider a system consisting of a one-dimensional lattice gas of electrons with a finite concentration of magnetic impurities. The host electrons propagate with nearest-neighbor hopping $t$, constrained by the excluded multiple occupancy of the lattice sites, and interact with electrons on neighboring sites via spin exchange $J$ and a charge interaction. The host is integrable at the supersymmetric point $J=2t$, where charges and spin form a SU(3) BBB permutation algebra (this differs from the graded FFB superalgebra of the traditional supersymmetric $t\ensuremath{-}J$ model, where B and F stand for boronic and fermionic degree of freedom). Without destroying the integrability, we introduce a finite concentration of impurities of arbitrary spin $S$, which hybridize with the conduction states of the host. We derive the Bethe ansatz equations diagonalizing the correlated host with impurities and discuss the ground-state properties as a function of magnetic field and the Kondo exchange coupling. While an isolated impurity of spin $Sg1/2$ has a magnetic ground state of effective spin $S\ensuremath{-}\frac{1}{2}$, a finite concentration introduces an additional Dirac sea (the impurity band), which gives rise to a singlet ground state. The impurities are antiferromagnetically correlated and frustrated in zero field. As a function of the field, first the narrow impurity band is spin polarized. The Van Hove singularities of the spin-rapidity bands define critical fields at which the susceptibility diverges. The impurities have in general mixed valent properties induced in part by the correlations in the host. Some of the aspects of the model are related to heavy-fermion alloys. A distribution of Kondo temperatures may give rise to non-Fermi-liquid properties.

Non-Fermi-liquid behavior in strongly correlated electron systems

Non-Fermi-liquid (NFL) behavior in three-dimensional metals with strong electron correlations can have different origins, viz. collective or single-ion effects. The former is manifest at a magnetic instability where the system changes from a nonmagnetic to a magnetic ground state as a function of some parameter like concentration or pressure. We review the properties of the exemplary NFL heavy-fermion system CeCu 6− x Au x at this magnetic instability, i.e. a logarithmic divergence of the specific-heat coefficient γ( T) = C/ T, a cusp in the magnetic DC susceptibility χ( T) for T → 0, and a T-linear contribution Δϱ to the electrical resistivity, as opposed to the Fermi-liquid behavior γ ∼ χ ≈ const, Δϱ ∼ T 2 found in many heavy-fermion systems, including the parent compound CeCu 6. Single-ion effects leading to NFL behavior are overscreening of magnetic or quadrupolar degrees of freedom of a magnetic impurity or a distribution of Kondo temperatures in a disordered alloy. Similarities and differences of the NFL phenomenology between these scenarios will be reviewed.

RECENT PROGRESS IN THE STUDY OF HEAVY-FERMION SYSTEMS

Recent experiments on heavy‐fermion systems have focused on the following issues: (i) non‐Fermi‐liquid behavior occurring either because of cooperative effects at a magnetic instability, i.e. at a T=0 phase transition between magnetically ordered and nonmagnetic groundstates driven by parameters such as chemical composition or pressure, or because of single‐ion effects such as the two‐channel Kondo effect or a distribution of Kondo temperatures; (ii) the symmetry of the order parameter in heavy‐fermion superconductors and the interplay of (often weak) magnetism and superconductivity. A review of recent developments in these areas is given.

Non-Fermi liquid behavior in metals

Metals are usually described within the framework of Fermi-liquid theory. Even heavy-fermion systems with their very large effective massm* derived from the huge linear specific-heat coefficient γ=C/T and a correspondingly large Pauli susceptibility χ can be regarded as Fermi-liquids withC/T ∼ χ=const. Recently, striking deviations from this behavior have been found in several heavy-fermion systems, e.g.C/T∼−ln(T/T0). This non-Fermi-liquid behavior may have different microscopic origins such as the single-ion quadrupolar Kondo effect, a collective effect caused by the incipient antiferromagnetic order or, simply a distribution of Kondo temperatures. Recent experiments will be reviewed with focus on the scenario of incipient magnetic order as exemplified in CeCu6−xAux.

Non-Fermi-liquid behavior in heavy-fermion systems

While many heavy-fermion systems can be described as Fermi liquid at very low temperatures ( T → 0), remarkable deviations in the thermodynamic (specific heat, magnetization) and transport properties (resistivity) have been observed recently in a number of systems. We review the experimental evidence for this ‘non-Fermi-liquid’ behavior which can be brought about by different microscopic origins. In particular, single-ion phenomena such as the two-channel quadrupolar Kondo effect or a distribution of Kondo temperatures, or collective phenomena such as the proximity to magnetic order at a zero-temperature quantum phase transition are discussed. These different routes to non-Fermi-liquid behavior are illustrated by examples of different systems.