Two energy scales and breakdown of renormalizability in the Kondo problem

It is shown that a second energy scale T ₀ ≫ T _k arises in the Kondo problem. Perturbation theory is valid only in the region T > T ₀. For this reason, the transition from weak to strong coupling occurs at temperatures much higher than the Kondo temperature T _k. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 2, 106–111 (25 July 1999)     

The crossover from the free spin to the singlet groundstate in the kondo problem

We present a theory of the Kondo susceptibility X₀ and the impurity relaxation rate 1/T₁. The result interpolates smoothly between the perturbation theory at high temperatures and a finite X₀ and T₁ at low T. A fair agreement with Wilson's numerical diagonalization and with experimental data for CuFe alloys is obtained.     

Kondo effect and mesoscopic fluctuations

Two important themes in nanoscale physics in the last two decades are correlations between electrons and mesoscopic fluctuations. Here we review our recent work on the intersection of these two themes. The setting is the Kondo effect, a paradigmatic example of correlated electron physics, in a nanoscale system with mesoscopic fluctuations; in particular, we consider a small quantum dot coupled to a finite reservoir (which itself may be a large quantum dot). We discuss three aspects of this problem. First, in the high-temperature regime, we argue that a Kondo temperature T _k which takes into account the mesoscopic fluctuations is a relevant concept: for instance, physical properties are universal functions of T/T _k. Secondly, when the temperature is much less than the mean level spacing due to confinement, we characterize a natural cross-over from weak to strong coupling. This strong coupling regime is itself characterized by well-defined single-particle levels, as one can see from a Nozières Fermi-liquid theory argument. Finally, using a mean-field technique, we connect the mesoscopic fluctuations of the quasiparticles in the weak coupling regime to those at strong coupling.     

Pressure dependence of the Kondo resistance anomaly and the pair breaking effect in La-Ce alloys

The pressure dependence of the parr breaking effect and of the resistance anomaly was measured in LaCe alloys. The results indicate that the maximum in the pressure dependent pair breaking effect is due to a monotonic shift of the Kondo temperatureT _k with pressure from valuesT _k > ?T _c0 toT _k ?T _c0, whereT _c0 is the superconducting transition temperature of pure lanthanum.     

Yb-Based Kondo Lattices: Insight from 170Yb Mössbauer, Positive Muon and γ–γ Perturbed Angular Correlations Spectroscopies

The usefulness of local hyperfine techniques in the investigation of the physical properties of Kondo lattices is illustrated through three examples. First, we show how Mössbauer spectroscopy on ¹⁷⁰Yb down to very low temperature (0.025 K) provides evidence for the existence of an incommensurate modulated magnetic structure close to T=0 in YbPtAl; a modulated structure at T=0 is in principle forbidden for Kramers ions, but it is made possible in YbPtAl due to the presence of the Kondo coupling. Second, we present a μSR study of the Kondo insulator YbB₁₂, and we evidence the persistence of fluctuations of very small correlated Yb moments close to T=0. Third, we report on a study by Perturbed Angular Correlation spectroscopy on the isotope ¹⁷²Yb of the Kondo lattice Yb₂Co₃Ga₉, which is characterised by a high Kondo temperature (T ₀?260 K). Our aim was to compare, on a large temperature range, the thermal variations of the 4f quadrupole moment and of the magnetic susceptibility, to check whether the scaling property predicted by theory could be observed.     

Grüneisen parameter of cerium compounds with unstable 4f shells

We give experimental results of magnetic susceptibility, thermal expansion and elastic constant measurements for CeSn₃ and CePd₃. We interpret these results with a phenomenological scaling function for the free energy and we include a brief discussion of CeAl₃. The coupling between the electronic system and the lattice can be described by an electronic Grüneisen parameter Ω_g associated with the unstable 4f system which turns out to become a system specific constant far below the fluctuation temperatureT ₀. The coupling parameter T₀Ω_g is an order of magnitude larger than the coupling constant for stable valentRE systems extracted from crystal field effects. A generalization to include magnetic field dependent effects is also given.     

Kondo effect,spin dynamics and magnetism in anomalous rare earth and actinide compounds

The problem of magnetic ordering in Kondo lattices is discussed. Criteria of ferro- and antiferromagnetism in the mean-field approximation for thes-f exchange model are obtained. In the case of a constant bare DOS, the saturated Kondo ferromagnetic solution is energetically stable at small intersite interactionsJ. The role of spin-fluctuation corrections at lowT _K in the building up the low-energy scale and the ground state magnetization is considered. Renormalization of spin-fluctuation frequencies atT>T _K is calculated. A possible picture of the formation of magnetism is presented starting from the high-T limit.     

Electrical resistivity and magnetoresistance of (NiAl)1−xMx,M = 3d transition metals23

Transport properties were investigated in (NiAl)_1?xM_x, M = 3d transition metals, in order to examine the extrinsic nature of NiAl. Experimental results are well described by the s?d exchange (Kondo) theory from which exchange energy J, Kondo temperature T_k, and spin value S were estimated. A comparison between our results and the results from dilute alloys is made.     

Numerical renormalization group studies of SU(4) Kondo effect in quantum dots

We theoretically study an enhancement of the Kondo effect in quantum dots with two orbitals and spin . The Kondo temperature and conductance are evaluated as functions of energy difference Δ between the orbitals, using the numerical renormalization group method. The Kondo temperature is maximal around the degeneracy point (Δ=0) and decreases with increasing |Δ| following a power law, T_K(Δ)=T_K(0)(T_K(0)/|Δ|)^γ, which is consistent with the scaling analysis. The conductance at T=0 is almost constant 2e²/h. Both the orbitals contribute to the conductance around Δ=0, whereas the current through the upper orbital is negligibly small when |Δ|T_K(0). These are characteristics of SU(4) Kondo effect.     

稀磁合金的杂质互作用效应

本文用格林函数方法讨论Tk(Kondo温度)时杂质互作用对Kondo效应的影响。对s-d互作用哈密顿量作自洽场近似时,同时计入导致Kondo效应和产生杂质互作用的切断项,求得了杂质系统的Kondo温度和低温电阻。结果表明:在稀磁合金中,杂质间的互作用效应使Kondo温度下降,并且使T《T_k时的电阻率温度变化曲线由(1-AT²)型变为(1+BT²)型(A,B>0),从而可能在Tk温区产生电阻极大。 关键词：     

Theory of magnetic impurities in superconductors. I

The Nagaoka Green's functions equations for a superconductor are solved exactly and the question of bound states within the gap is answered unambiguously. It is shown that there are always two bound states symmetrically located with respect to the center of the gap. For ferromagnetic coupling,γ>0, and for antiferromagnetic coupling, butT _K ?T _c0 orT _K ?T _c0, these bound states are very close to the gap edges. ForT _K ～T _c 0, however, the bound states move towards the center of the gap. It is pointed out that in the latter case important deviations from the Abrikosov-Gorkov theory, i.e. manifestations of the Kondo effect, should occur which could be tested experimentally by investigating the density of states.     

On the mechanism of decomposition of the benzyl radical

The C₇H₇ potential energy surface was studied from first principles to determine the benzyl radical decomposition mechanism. The investigated high temperature reaction pathway involves 15 accessible energy wells connected by 25 transition states. The analysis of the potential energy surface, performed determining kinetic constants of each elementary reaction using conventional transition state theory, evidenced that the reaction mechanism has as rate determining step the isomerization of the 1,3-cyclopentadiene, 5-vinyl radical to the 2-cyclopentene,5-ethenylidene radical and that the fastest reaction channel is dissociation to fulvenallene and hydrogen. This is in agreement with the literature evidences reporting that benzyl decomposes to hydrogen and a C₇H₆ species. The benzyl high-pressure decomposition rate constant estimated assuming equilibrium between the rate determining step transition state and benzyl is k₁(T) = 1.44 × 10¹³T^0.453exp(−38400/T) s⁻¹, in good agreement with the literature data. As fulvenallene reactivity is mostly unknown, we investigated its reaction with hydrogen, which has been proposed in the literature as a possible decomposition route. The reaction proceeds fast both backward to form again benzyl and, if hydrogen adds to allene, forward toward the decomposition into the cyclopentadienyl radical and acetylene with high-pressure kinetic constants k₂(T) = 8.82 × 10⁸T^1.20exp(1016/T) and k₃(T) = 1.06 × 10⁸T^1.35exp(1716/T) cm³/mol/s, respectively. The computed rate constants were then inserted in a detailed kinetic mechanism and used to simulate shock tube literature experiments.     

非晶态超导体的2△0/(kBTc)和声子谱参量

提出了能够很好地描述非过渡金属无序和非晶态超导体的2Δ₀/(k_BT_c)与声子谱参量之间关系的一个公式:2Δ₀(k_BT_c=4.95[1-(T₀<ω>^1/2)/A(1/(λω₀)+1/(20λ<ω>)+1/(20<ω>))]。计算了大量已知声子谱的非晶和无序超导体的能隙2Δ₀对T_c的比,结果表明在百分之几的范围内与实验值符合。指出了非过渡金属和合金的非晶态超导体,既可以是一个2Δ₀/(k_BT_c)值远大于BCS理论值(3.53)的强耦合超导体,也可以是一个2Δ₀/(k_BT_c)值比BCS理论值还要小得多的弱耦合超导体。 关键词：     

Universal temperature corrections to the free energy for the gravitational field

The temperature correction to the free energy of the gravitational field is considered which does not depend on the Planck energy physics. The leading correction may be interpreted in terms of the temperature-dependent effective gravitational constant G_eff. The temperature correction to appears to be valid for all temperatures T?E_Planck. It is universal since it is determined only by the number of fermionic and bosonic fields with masses m?T, does not contain the Planck energy scale E_Planck which determines the gravitational constant at T=0, and does not depend on whether or not the gravitational field obeys the Einstein equations. That is why this universal modification of the free energy for gravitational field can be used to study thermodynamics of quantum systems in condensed matter (such as quantum liquids superfluid ³He and ⁴He), where the effective gravity emerging for fermionic and/or bosonic quasiparticles in the low-energy corner is quite different from the Einstein gravity.     

Sb-NMR/NQR study of CeIrSb

We report Sb-NMR/NQR measurements on a valence fluctuating compound CeIrSb, which is isostructural to the Kondo semiconductors CeRhSb and CeNiSn. The nuclear spin-lattice relaxation rate divided by temperature, 1/T₁T has a maximum around 300 K and considerably decreases in proportion to T² when cooling down, followed by a 1/T₁T∼const. behavior below 20 K. These results indicate that CeIrSb has a V-shaped pseudogap with a residual density of states at the Fermi level. The size of pseudogap for CeIrSb is estimated to be about 350 K, which is one order of magnitude larger than the values of 28 K for CeRhSb and 14 K for CeNiSn. The larger size of energy gap in CeIrSb may be attributed to much stronger c-f hybridization than those for CeRhSb and CeNiSn.     

Resistance maximum across the spin glass to Kondo transition

In a recent theory of the noise model of alloys like AuFe a singular point at zero temperature was found to separate a spin glass phase at high concentrations and a Kondo phase at low concentrations. Despite this there is a resistance maximum in both “phases”, although of different characters. In the present letter a relation is given between the temperature of the maximum, T_m, the noise temperature, Δ_c, and the Kondo temperature, T_K. This extends a previously given expression, that is only valid in the spin glass limit Δ_c >> T_K, across the transition at Δ_c = T_K into the Kondo phase and values of Δ_c less than T_K.     

Transport across an Anderson quantum dot in the intermediate coupling regime

We describe linear and nonlinear transport across a strongly interacting single impurity Anderson model quantum dot with intermediate coupling to the leads, i.e. with tunnel coupling Γ of the order of the thermal energy k _B T. The coupling is large enough that sequential tunneling processes (second order in the tunneling Hamiltonian) alone do not suffice to properly describe the transport characteristics. Upon applying a density matrix approach, the current is expressed in terms of rates obtained by considering a very small class of diagrams which dress the sequential tunneling processes by charge fluctuations. We call this the “dressed second order” (DSO) approximation. One advantage of the DSO is that, still in the Coulomb blockade regime, it can describe the crossover from thermally broadened to tunneling broadened conductance peaks. When the temperature is decreased even further (k _B T < Γ), the DSO captures Kondesque behaviours of the Anderson quantum dot qualitatively: we find a zero bias anomaly of the differential conductance versus applied bias, an enhancement of the conductance with decreasing temperature as well as universality of the shape of the conductance as function of the temperature. We can without complications address the case of a spin degenerate level split energetically by a magnetic field. In case spin dependent chemical potentials are assumed and only one of the four chemical potentials is varied, the DSO yields in principle only one resonance. This seems to be in agreement with experiments with pseudo spin [U. Wilhelm, J. Schmid, J. Weis, K.V. Klitzing, Physica E 14, 385 (2002)]. Furthermore, we get qualitative agreement with experimental data showing a cross-over from the Kondo to the empty orbital regime.     

Liquid Madelung energy and Schottky defect energy related to liquid structure and melting temperature for alkali halides

Motivated by the work of Reiss et al in which the melting temperature T_m of alkali halides is correlated with Coulomb energy, we consider the cohesive energy W of ionic melts and Schottky defect energy E_s in the hot crystal, relative to the thermal energy k_BT_m It is shown here that W is accurately approximated by the liquid Madelung energy and hence that Wk_BT_m relates to the charge-charge direct correlation function c_QQ(r) at r = 0 The existence of a “Madelung constant” for the liquid at T_m is thereby demonstrated through the alkali halide series An estimate of the ratio E_s/k_BT_m then considered, the basic additional ingredient being argued to be the static dielectric constant of the solid The BarrDawson-Lidiard empirical correlation between E_s, and k_BT_m can be understood in this way.     

Evaluation of the formation entropy of a single vacancy by means of positron annihilation

Analyzing positron annihilation data it was found that the formation energy of a single vacancy is proportional to the characteristic temperature T_c in f.c.c. metals. Assuming that the equilibrium fractional concentrations of single vacancies at T_c are constant, one finds that the formation entropy of a single vacancy is (1.6 ± 0.1)k for all f.c.c. metals. For zinc and cadmium, the formation entropies are 2.5k and 3.3k respectively.