Stabilization of mixed valence by polaronic effects

Polaronic effects in mixed valence systems are studied in a simple model of localized d-electrons for arbitrary values of relevant parameters. Variational approach is used which permits one to interpolate between the limit of average static lattice distortion and that of different local distortions for different valence states of an ion. It is shown that the degree of local electron-lattice correlation and polaron narrowing of virtual f-level changes with a position of f-level. Polaronic effects make a valence transition more gradual and stabilize mixed valence phase. At the end some comments on a possibility of Valence Density Waves in mixed valence compounds are made and certain properties of CeAl₂ are tentatively ascribed to them.     

The role of fluctuations in mixed valence compounds

Previous renormalization group results for a simple spinless mixed valence model yielded large intersite ?-electron correlations if extended coherent hybridization mixed valence states are assumed. We simulate these correlations by an ?-level energy distribution and analyze its consequences. It is seen that a relatively small distribution width already smears the coherent hybridization gap leading to a lattice of essentially independent resonant levels.     

“Influence of valence instabilities on the Curie-temperature of ferromagnetic 4f-systems”

We inspect the stability of ferromagnetism in 4f-systems, which have an insulating, ferromagnetic ground state in the integral valent phase and fluctuate between a magnetic and a nonmagnetic configuration in the intermediate valent phase. It turns out that for large gaps between 4f-level and lower edge of the empty conduction band ferromagnetism is created by a certain interplay between the s-f hybridization, which allows real or virtual electron transitions between f-level and conduction band, and the s-f exchange interaction, which mediates an indirect coupling between the localized 4f-moments. When the gap is reduced by external pressure or by alloying with proper impurities the local f-moment becomes steadily quenched while simultaneously the coupling between the more and more reduced moments is drastically enhanced. These two competitive effects lead to a distinct maximum of the Curie-temperature just in the intermediate valence phase.     

Fermi liquid theory for a simple mixed valence impurity model

Using Ward identities we relate the low temperature charge susceptibility and the specific heat for a simple spinless mixed valence impurity. The results are compared with previous ones for the Anderson model and the Kondo problem.     

From mixed valence to the Kondo lattice regime

Many heavy fermion materials are known to cross over from the Kondo lattice regime to the mixed valence regime or vice versa as a function of pressure or doping. We study this crossover theoretically by employing the periodic Anderson model within the framework of the dynamical mean field theory. Changes occurring in the dynamics and transport across this crossover are highlighted. As the valence is decreased (increased) relative to the Kondo lattice regime, the Kondo resonance broadens significantly, while the lower (upper) Hubbard band moves closer to the Fermi level. The resistivity develops a two peak structure in the mixed valence regime: a low temperature coherence peak and a high temperature 'Hubbard band' peak. These two peaks merge, yielding a broad shallow maximum upon decreasing the valence further. The optical conductivity likewise exhibits an unusual absorption feature (shoulder) in the deep mid-infrared region, which grows in intensity with decreasing valence. The involvement of the Hubbard bands in dc transport and of the effective f-level in the optical conductivity are shown to be responsible for the anomalous transport properties. A two-band hybridization-gap model, which neglects incoherent effects due to many-body scattering, commonly employed to understand the optical response in these materials is shown to be inadequate, especially in the mixed valence regime. Comparison of theory with experiment carried out for (a) dc resistivities of CeRhIn(5), Ce(2)Ni(3)Si(5), CeFeGe(3) and YbIr(2)Si(2), (b) pressure dependent resistivity of YbInAu(2) and CeCu(6), and (c) optical conductivity measurements in YbIr(2)Si(2) yields excellent agreement.     

Properties of SO(8) extended supergravity

The conjectured SU(8) invariance of the field equations of SO(8) extended supergravity is used to elucidate the general structure of the extended theories. Due to the representation content of the spinless fields this does not lead to a complete determination of the theory, as was the case for N = 4. The non-polynomial modifications by spinless fields are given in terms of a number of SU(8) covariant tensors, for which various identities are derived and discussed.     

Gutzwiller and slave-boson methods for intersite Coulomb interactions

We investigate the application of the slave-boson method to the treatment of finite intersite interactions. In the saddle-point approximation of the formalism the results obtained with an extended Gutzwiller-type local ansatz are recovered. We discuss the application of the method to a spinless fermion model with nearest-neighbor and long-range Coulomb interactions, respectively.     

A new mechanism of valence change transitions

Within the framework of the s-f hybridization model for f-metals it is shown that Kondo-type s-f scattering and f-electron damping lead to a peak in the f-electron density of states ?_f(ω). This peak arises directly above the chemical potential μ despite the deep position of the initial f-electron level ?_f relative to μ. The reconstruction of ?_f(ω) depends strongly on f-level degeneracy, temperature and pressure and it can initiate continuous or discontinuous valence change transition.     

Effect of the d-f coulomb correlation on the valence transition of intermediate valence systems

The d-f Coulomb repulsion, G, is treated by means of a real space decimation procedure on a Bethe lattice. The valence is calculated as a function of the relative position of the f-level with respect to the conduction band. No discontinuous transitions are found.     

A cluster-like approach for the valence transition in SmS compounds

The extended Falicov-Kimball model is applied to a cluster composed of three spinless ions. By one of these ions we simulate an interstitial impurity situation which often occurs in semiconducting SmS. The remaining two ions are taken as next nearest neighbours sitting on regular Sm lattice sites. For a proper choice of parameters these two ions may undergo a valence transition due to the presence of the impurity. The situation corresponding to an anionic impurity can be simulated in a similar way.     

Theory of valence mixing for rare-earth compounds

A theory for the mixed valence state of rare-earth compounds is presented. It includes the following features: (1) two types of electronic states-localized, highly correlated states and itinerant, non-correlated states; (2) a very strong Coulomb repulsion between localized states in the same site; (3) a Coulomb interaction between localized and itinerant states which drives the phase transition; and (4) hybridization between localized and itinerant states which produces the mixed valence state. It is shown that this model produces (a) at T = 0, a variation in the number of localized electrons which may vary in a smooth or in a discontinuous fashion as a function of pressure or alloying; (b) transitions at finite temperature which terminate in a classical critical point. Qualitative agreement with experiment is an encouraging feature of the model.     

On the pressure-temperature phase diagram of intermediate valence compounds

The pressure-temperature (P, T) phase diagram of intermediate valence compounds has been calculated on the basis of the periodic Anderson model which was extended to include the interaction of 4f electrons with longitudinal optical phonons. It is shown that the positive slope (dP/dT>0) of the phase boundary between the insulating and the mixed valence phase as observed experimentally in Sm S and many other systems is determined by the behaviour of the electronic density of states of the interacting system as function ofP. Moreover, the observed anomalous thermal contraction in the insulating phase near the phase boundary and the anomalously large thermal expansion in the metallic phase are well described by numerical results for the extended periodic Anderson model.     

All-electron GW approximation with the mixed basis expansion based on the full-potential LMTO method

We present a new all-electron, augmented-wave implementation of the GW approximation using eigenfunctions generated by a recent variant of the full-potential LMTO method. The dynamically screened Coulomb interaction W is expanded in a mixed basis set which consists of two contributions, local atom-centered functions confined to muffin-tin spheres, and plane waves with the overlap to the local functions projected out. The former can include any of the core states; thus the core and valence states can be treated on an equal footing. Systematic studies of semiconductors and insulators show that the GW fundamental bandgaps consistently fall low in comparison to experiment. Also the quasi-particle (QP) levels differ significantly from other, approximate methods, in particular those that approximate the core with a pseudopotential, or those that include valence states only.     

Valence transition behavior of the doped Falicov-Kimball model at nonzero temperatures

The extrapolation of small-cluster exact-diagonalization calculations is used to study the influence of doping on valence transitions in the spinless Falicov-Kimball model at nonzero temperatures. Two types of doping are examined, and namely, the substitution of rare-earth ions by nonmagnetic ions that introduce (i) one or (ii) none additional electron (per nonmagnetic ion) into the conduction band. It is found that the first type of substitution increases the average f-state occupancy of rare-earth ions, whereas the second type of substitution has the opposite effect. The results obtained are used to describe valence transition behavior of samarium in the hexaboride solid solutions Sm_1−xM_xB₆ (M=Y³⁺, La³⁺, Sr²⁺, Yb²⁺) and a very good agreement of theoretical and experimental results is found.     

Role of hybridization in phase transition in the Falicov-Kimball model

Extended Falicov-Kimball model has been considered for samarium-chalcogenides where, (a) f-f interactions are considered to be quite large, (b) periodicity of the system has been taken into account, (c) f-d interactions are considered within mean field approximation and (d) the unperturbed conduction bandwidth is taken to be non-zero. We observe both continuous as well as discontinuous transitions and hence conclude that “extended Falicov-Kimball model” is a suitable model which can describe both a first order transition and a suitable intermediate valence phase in Sm-chalcogenides.     

Weak-coupling treatment of electronic (anti-)ferroelectricity in the extended Falicov-Kimball model

We study the (spinless) Falicov-Kimball model extended by a finite band width (hopping t _f ) of the localized (f-) electrons in infinite dimensions in the weak-coupling limit of a small local interband Coulomb correlation U for half filling. In the case of overlapping conduction- and f-bands different kinds of ordered solutions are possible, namely charge-density wave (CDW) order, electronic ferroelectricity (EFE) and electronic antiferroelectricity (EAFE). The order parameters are calculated as a function of the model parameters and of the temperature. There is a first-order phase transition from the CDW-phase to the EFE- or EAFE-phase. The total energy is calculated to determine the thermodynamically stable solution. The quantum phase diagrams are calculated.     

Role of correlated hopping in mixed valence phenomena

Role of correlated hopping is studied using extended Falicov–Kimball model in a small cluster. A discontinuous insulator-to-metal transition is observed at a critical f-level energy. Transition is sharper for larger correlated hopping. In the specific heat curves a two-peak structure consisting of a sharp peak followed by a Schottky-type broad peak is exhibited. In a limited parameter region, some heavy-fermion like characteristics have been observed.     

Electron-phonon coupling in intrinsic trans-polyacetylene

We consider a valence force field model for the phonon spectrum of (CH)_x and find that phonon coupling to extended π electron states must be included to describe the observed Raman active modes of the polymer. The calculated phonon spectra are shown to possess the zone center dispersion anomalies characteristic of a condensed Peierls ground state.     

Form factors and correlation functions of an interacting spinless fermion model

Introducing the fermionic R-operator and solutions of the inverse scattering problem for local fermion operators, we derive a multiple integral representation for zero-temperature correlation functions of a one-dimensional interacting spinless fermion model. Correlation functions particularly considered are the one-particle Green's function and the density–density correlation function both for any interaction strength and for arbitrary particle densities. In particular for the free fermion model, our formulae reproduce the known exact results. Form factors of local fermion operators are also calculated for a finite system.