Recent progress in theoretical understanding of heavy fermion systems

A key to understand the physics of heavy Fermion systems is the competition between the RKKY interaction and the Kondo screening effect of magnetic moments. The Kondo lattice model is a theoretical model for which one can study the interplay. Recently the ground state phase diagram of the one‐dimensional Kondo lattice model has been completed. After reviewing the properties of the three phases in the phase diagram we discuss the Kondo insulator in one‐dimension with particular emphasis on the difference between the spin excitation gap and the charge excitation gap. We argue that the Kondo insulators may be distinguished from the ordinary band insulators by the difference between the two gaps. Another topic which is discussed in this article is the complicated magnetic phase diagram of the low‐carrier‐density system of cerium monopnictides. We propose that the new mechanism which exists for Kondo semimetals may be responsible for the complicated magnetic structures in these compounds. This revised version was published online in July 2006 with corrections to the Cover Date.     

Heavy fermion semiconductors

The heavy fermion semiconductors, or Kondo insulators, are very narrow gap semiconductors in which the properties show unusual temperature dependencies. We shall review their properties and show how they can be interpreted in terms of an electronic band structure, with a temperature dependent hybridization gap together with temperature dependent quasi-particle lifetimes. The properties of these semiconductors are very sensitive to impurities, which can enhance the incipient antiferromagnetic correlations and precipitate a magnetic instability.     

Field induced magnetic ordering transition in Kondo insulators

We study the 2D Kondo insulators in a uniform magnetic field using quantum Monte Carlo simulations of the particle-hole symmetric Kondo lattice model and a mean field analysis of the Periodic Anderson model. We find that the field induces a transition to an insulating, antiferromagnetically ordered phase with staggered moment in the plane perpendicular to the field. For fields in excess of the quasi-particle gap, corresponding to a metal in a simple band picture of the periodic Anderson model, we find that the metallic phase is unstable towards the spin density wave type ordering for any finite value of the interaction strength. This can be understood as a consequence of the perfect nesting of the particle and hole Fermi surfaces that emerge as the field closes the gap. We propose a phase diagram and investigate the quasi-particle and charge excitations in the magnetic field. We find good agreement between the mean-field and quantum Monte Carlo results.Received: 17 December 2003, Published online: 8 June 2004PACS: 71.27. + a Strongly correlated electron systems; heavy fermions - 71.10.Fd Lattice fermion models (Hubbard model, etc.) - 71.30. + h Metal-insulator transitions and other electronic transitions - 75.30.Mb Valence fluctuation, Kondo lattice, and heavy-fermion phenomena - 75.30.Fv Spin-density waves     

稀磁合金中“电阻极大”现象的双杂质散射理论

本文基于s-d相互作用,考虑杂质之间存在RKKY相互作用,提出了一种新的双杂质散射模型。按照这个模型,当一个杂质作自旋翻转散射时,由于杂质之间存在着RKKY关联,它的自旋作为内部自由度会受到限制。由于这种关联,抑制了杂质的自旋翻转散射,结合Kondo的logT项,能形成电阻极大。本文计算了所有可能的“DIS”图(双杂质自能图),在Kondo电阻公式中加入了A/(T₀²—T²)这样的项。其中A是一个正常数。T₀是一个临界温度。当T≤T₀时,这个公式不再有意义。这个理论和已有的分子场理论在本质上是不同的.因为它并不依赖于合金中的磁有序.因此当T≥T_c时(T_c是磁有序转变温度),这种机制仍起作用,但分子场理论则不行.这是一种顺磁效应.我们和Cd-Mn(杂质浓度从0.01到0.1at./0)的实验曲线进行了比较,发现符合得很好.最后,我们认为即使在极低浓度下这种机制也是消除Kondo logT发散的主要原因. 关键词：     

Anomalous magnetic splitting of the kondo resonance

The splitting of the Kondo resonance in the density of states of an Anderson impurity in a finite magnetic field is calculated from the exact Bethe-ansatz solution. The result gives an estimate of the electron spectral function for a nonzero magnetic field and the Kondo temperature, with consequences for transport experiments on quantum dots in the Kondo regime. The strong correlations of the Kondo ground state cause a significant low-temperature reduction of the peak splitting. Explicit formulas are found for the shift and broadening of the Kondo peaks. A likely cause of the problems of large- N approaches to spin- 1 / 2 impurities at finite magnetic field is suggested.     

Kondo effect in the presence of magnetic impurities

We measure transport through gold grain quantum dots fabricated using electromigration, with magnetic impurities in the leads. A Kondo interaction is observed between dot and leads, but the presence of magnetic impurities results in a gate-dependent zero-bias conductance peak that is split due to a RKKY interaction between the spin of the dot and the static spins of the impurities. A magnetic field restores the single Kondo peak in the case of an antiferromagnetic RKKY interaction. This system provides a new platform to study Kondo and RKKY interactions in metals at the level of a single spin.     

Effect of magnetic impurities on energy exchange between electrons

In order to probe quantitatively the effect of Kondo impurities on energy exchange between electrons in metals, we have compared measurements on two silver wires with dilute magnetic impurities (manganese) introduced in one of them. The measurement of the temperature dependence of the electron phase coherence time on the wires provides an independent determination of the impurity concentration. Quantitative agreement on the energy exchange rate is found with a theory by G?ppert et al. that accounts for Kondo scattering of electrons on spin-1/2 impurities.     

The Kondo effect of a magnetic impurity under the crystalline field

Using the Coqblin-Schrieffer exchange interaction, we investigate the Kondo effect for a magnetic impurity under the crystalline field, as occuring in La or Y alloys containing cerium impurities. The Hamann typet-matrix equation for the conduction electron scattered by a magnetic impurity is derived and solved, using the method of Zittarz and Müller-Hartmann. We find a Kondo type anomaly and a decreased Kondo temperature due to the crystalline field splittings. The resistivity, entropy and specific heat are calculated and they show some characteristic behavior due to the crystalline field splittings.     

Magnetic-field-dependent quasiparticle energy relaxation in mesoscopic wires

In order to find out if magnetic impurities can mediate interactions between quasiparticles in metals, we have measured the effect of a magnetic field B on the energy distribution function f(E) of quasiparticles in two silver wires driven out of equilibrium by a bias voltage U. In a sample showing sharp distributions at B=0, no magnetic field effect is found, whereas, in the other sample, rounded distributions at low magnetic field get sharper as B is increased, with a characteristic field proportional to U. Comparison is made with recent calculations of the effect of magnetic-impurities-mediated interactions taking into account Kondo physics.     

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.     

Random field effects in field-driven quantum critical points

We investigate the role of disorder for field-driven quantum phase transitions of metallic antiferromagnets. For systems with sufficiently low symmetry, the combination of a uniform external field and non-magnetic impurities leads effectively to a random magnetic field which strongly modifies the behavior close to the critical point. Using perturbative renormalization group, we investigate in which regime of the phase diagram the disorder affects critical properties. In heavy fermion systems where even weak disorder can lead to strong fluctuations of the local Kondo temperature, the random field effects are especially pronounced. We study possible manifestation of random field effects in experiments and discuss in this light neutron scattering results for the field driven quantum phase transition in CeCu_5.8Au_0.2.     

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.     

Evolution of the Fermi surface across a magnetic order-disorder transition in the two-dimensional Kondo lattice model: a dynamical cluster approach

We use the dynamical cluster approximation, with a quantum Monte Carlo cluster solver on clusters of up to 16 orbitals, to investigate the evolution of the Fermi surface across the magnetic order-disorder transition in the two-dimensional doped Kondo lattice model. In the paramagnetic phase, we observe the generic hybridized heavy-fermion band structure with large Luttinger volume. In the antiferromagnetic phase, the heavy-fermion band drops below the Fermi surface giving way to hole pockets centered around k=(pi/2,pi/2) and equivalent points. In this phase Kondo screening does not break down, but the topology of the resulting Fermi surface is that of a spin-density wave approximation in which the localized spins are frozen.     

The effect of magnetic impurity scattering in Au films

The magnetic impurity scattering plays an important role in the phase coherence behavior of thin films.By using the thickness and disorder dependences of the low temperature logarithmic anomaly in resistivity we are able to determine the concentration of magnetic impurities in Au films and demonstrate that the low temperature saturation or plateau in phase decoherence time is closely related with the Kondo effect.     

Spectroscopic and magnetic mirages of impurities in nanoscopic systems with focusing properties

We study the behavior of magnetic impurities in nanoscopic systems with focusing properties. In this paper, we analyze the spectroscopic and magnetic properties of Kondo, intermediate valence and magnetic impurities on a sphere with a metallic surface. Using exact calculations, we obtain important spectroscopic and magnetic mirages at the antipodes of the impurity location. When compared with calculations performed using effective models our results validate previous calculations of spectroscopic mirages. These calculations can be extended to other systems with focusing properties like quantum corrals where a similar behavior is expected.     

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.     

Scaling of the low-temperature dephasing rate in Kondo systems

We present phase coherence time measurements in quasi-one-dimensional Ag wires doped with Fe Kondo impurities of different concentrations n_{s}. Because of the relatively high Kondo temperature T_{K} approximately 4.3 K of this system, we are able to explore a temperature range from above T_{K} down to below 0.01T_{K}. We show that the magnetic contribution to the dephasing rate gamma_{m} per impurity is described by a single, universal curve when plotted as a function of T/T_{K}. For T>0.1T_{K}, the dephasing rate is remarkably well described by recent numerical results for spin S=1/2 impurities. At lower temperature, we observe deviations from this theory. Based on a comparison with theoretical calculations for S>1/2, we discuss possible explanations for the observed deviations.     

Theory of the fano resonance in the STM tunneling density of states due to a single kondo impurity

The conduction electron density of states nearby single magnetic impurities, as measured recently by scanning tunneling microscopy (STM), is calculated, taking into account tunneling into conduction electron states only. The Kondo effect induces a narrow Fano resonance in the conduction electron density of states. The line shape varies with the distance between STM tip and impurity, in qualitative agreement with experiments, but is very sensitive to details of the band structure. For a Co impurity the experimentally observed width and shift of the Kondo resonance are in accordance with those obtained from a combination of band structure and strongly correlated calculations.     

Topological response theory of doped topological insulators

We generalize the topological response theory of three-dimensional topological insulators (TI) to metallic systems-specifically, doped TI with finite bulk carrier density and a time-reversal symmetry breaking field near the surface. We show that there is an inhomogeneity-induced Berry phase contribution to the surface Hall conductivity that is completely determined by the occupied states and is independent of other details such as band dispersion and impurities. In the limit of zero bulk carrier density, this intrinsic surface Hall conductivity reduces to the half-integer quantized surface Hall conductivity of TI. Based on our theory we predict the behavior of the surface Hall conductivity for a doped topological insulator with a top gate, which can be directly compared with experiments.     

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.