Peter Fulde

Theory of Heavy Fermion Systems

Publisher Summary The chapter presents a study on theory of heavy fermion systems. In the heavy fermion systems it seems that some of the features of the single Kondo impurity problem appear in an enhanced form simply, because there is at least one magnetic ion per unit cell. Therefore, the heavy fermion systems have sometimes been referred to as “lattices of Kondo ions” or “Kondo lattice systems.” The chapter presents a discussion on quasiparticle-phonon interactions and presents a demonstration that elastic properties of heavy fermion systems are almost as interesting as the electronic ones. Superconducting heavy fermion systems have attracted great interest, because they are considered as possible candidates for unconventional pairing. An outstanding experimental finding is the power-law behavior of the low temperature specific heat, thermal conductivity, ultrasonic attenuation, and nuclear magnetic resonance (NMR) relaxation rate in those systems. The chapter also presents a figure based on the scenario within which the heavy fermion systems should be viewed. It shows the different degrees of electron correlations in solids. The heavy fermion systems are the ones, which come closest to the localization limit, in which electron correlations exclude any charge fluctuations within the f shell.

On the computation of electronic correlation energies within the local approach

A recently developed local approach to the computation of electron‐correlation energies is extended and investigated in great detail. For that purpose it is applied to the Ne atom and the CH4 molecule for which correlation‐energy calculations are available. It is shown that the local approach exhausts up to a few percent the correlation energy which is obtainable within a given basis set. A detailed comparison with conventional CI methods reveals the advantages of the present approach. Only a fraction of the two‐electron matrix elements Vijkl has to be calculated, and the number of required configurations is drastically reduced. Furthermore, CH4 is used as an example to demonstrate that the correlation‐energy calculations for large systems can be broken up into ones for small systems.

Theoretical models for superionic conductors

Abstract The present theoretical understanding of various properties of superionic conductors is reviewed. Emphasis is put on their treatment as classical many-particle systems and on the analysis of their dynamic behaviour. Different kinds of approaches pertaining to the low frequency dynamics are considered in detail. They include stochastic models, like hopping or Fokker-Planck models as well as a hydrodynamic theory. The high frequency (phonon-) dynamics and the information obtained from computer simulations is also analysed. As far as possible, the relevance of the different approaches with respect to experiments on specific materials is discussed. Possible directions for future investigations are outlined.

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 temperatureTc produces the right order of magnitude.

Ground state calculations of di-π-cyclooctatetraene cerium

Quantum chemical calculations are presented which predict that in the ground state of di‐π‐cyclooctatetraene cerium (cerocene) the Ce ion is almost entirely in a 4f1 configuration corresponding to Ce3⊕(C8H1.5■8)2. The 4f electron forms with an electron of the ligand e2u highest‐occupied molecular orbital a 4f1e32u singlet in close analogy to a Kondo ion in a metal. Due to coupling of the 4f1e32u with the 4f0e42u configuration, the latter corresponding to Ce4⊕(C8H2≤8)2, the splitting between the ground state singlet and the first excited triplet is of the order 0.5 eV. The self‐consistent‐field and multiconfiguration self‐consistent‐field parts of the calculations are done by employing recently developed pseudopotentials for cerium using basis sets of up to 626 basis functions. The correlation energy is accounted for by means of various correlation‐energy density functionals and also by limited coupled electron‐pair approximation calculations. Similar results are found in both cases.

Magnetic excitations in crystal-field split 4f systems

Abstract A survey is given of magnetic excitations in metallic 4f systems when the crystal-field splitting is comparable to or larger than the magnetic interaction between different sites. Particular emphasis is put on the interaction of crystal-field split rare-earth ions with conduction electrons. A number of physical effects is discussed which result from that interaction. The modifications of the magnetic excitations are described which result when the coupling of phonons to the crystal-field levels is so strong that a bound state between the two types of excitations is formed. For a study of these phenomena the method of neutron scattering is an indispensable tool. For that reason it plays a central part in this review.

Some crystalline field effects in metals

Abstract We discuss different physical effects which are caused by the crystalline electric field splitting of rare earth ions in metals. Thus, the rare earth ions may be impurities dissolved in a metallic matrix or they may form a regular lattice. In the former case we distinguish between the cases of a normal conducting and a superconducting matrix. The influence of the crystalline field splitting on the properties of the conduction electrons is calculated. In the case of a normal matrix anomalous behaviour of the thermoelectric power is found due to the impurity levels. If the matrix is superconducting large deviations result from the theory of Abrikosov and Gorkov which describes the influence of non-split magnetic impurities on superconductivity. A comparison of the theory with available experiments is presented. For the case that the rare earth ions form a regular lattice we discuss various aspects of the collective excitations in the paramagnetic state. Special attention is paid to the soft mode pr...

On the accuracy of correlation-energy expansions in terms of local increments

The incremental scheme for obtaining the energetic properties of extended systems from wave-function-based ab initio calculations of small (embedded) building blocks, which has been applied to a variety of van der Waals-bound, ionic, and covalent solids in the past few years, is critically reviewed. Its accuracy is assessed by means of model calculations for finite systems, and the prospects for applying it to delocalized systems are given.

Formally tetravalent cerium and thorium compounds: a configuration interaction study of cerocene Ce(C8H8)2 and thorocene Th(C8H8)2 using energy-adjusted quasirelativistic ab initio pseudopotentials

Abstract Large-scale state-averaged multi-configuration self-consistent field, configuration interaction, averaged coupled-pair functional and spin-orbit configuration interaction calculations have been carried out for the ground states and low-lying excited states of the bis(cyclooctatetraene)f-element sandwich complexes cerocene Ce(C 8 H 8 ) 2 and thorocene Th(C 8 H 8 ) 2 . Whereas for a single-determinant wavefunction thorocene may be pictured as a Th IV compound, i.e. a Th 4+ closed-shell ion complexed by two aromatic C 8 H 8 2− ligands, cerocene is to a first approximation a Ce III compound, i.e. a Ce 3+ ion with a 4f 1 configuration and two C 8 H 8 1.5− ligands. When cerocene is described by a multi-determinant wavefunction admixture of the Ce 4+ (C 8 H 8 2− ) 2 configuration leads to a 1 A 1g ground state of the same symmetry as in thorocene. For both compounds results for the metal-ring distance, the symmetric metal-ring stretching frequency, the photoelectron spectrum and the optical spectrum are compared to experimental data.

Superconductors containing impurities with crystal-field split energy levels

We investigate theoretically the problem of a superconducting matrix containing paramagnetic rare earth impurities with crystal-field split energy levels. There are two competing mechanisms which change the superconducting transition temperatureTc. One is inelastic charge scattering of conduction electrons from the aspherical part of the 4f charge distribution, which leads to an increase inTc similar to that of optical phonons. The other and often predominant mechanism comes from the exchange interaction, which depressesTc and can be very effective even among non-magnetic levels via off-diagonal matrix elements. Crystalline fields serve to alter the effectiveness of the two kinds of scattering depending upon the symmetry character of the low-lying levels, and in favorable cases one may study separately the effects of the two types of scattering by adding different impurities to a given host. We find that crystal-field levels at energies quite high compared tokB·Tc can still have an important effect onTc. It is shown that the crystalline-field splitting should be directly observable as structure in the tunneling characteristics.