Thermodynamic potential of the Periodic Anderson Model with the X-boson method: Chain Approximation

The Periodic Anderson Model (PAM) in the $U\to\infty$ limit has been studied in a previous work employing the cumulant expansion with the hybridization as perturbation (M. S. Figueira, M. E. Foglio and G. G. Martinez, Phys. Rev. B \textbf{50}, 17933 (1994)). When the total number of electrons $N_{t}$ is calculated as a function of the chemical potential $\mu$ in the ``Chain Approximation'' (CHA), there are three values of the chemical potential $\mu$ for each $N_{t}$ in a small interval of $N_{t}$ at low $T$ (M. S Figueira, M. E Foglio, Physica A 208 (1994)). We have recently introduced the ``X-boson'' method, inspired in the slave boson technique of Coleman, that solves the problem of non conservation of probability (completeness) in the CHA as well as removing the spurious phase transitions that appear with the slave boson method in the mean field approximation. In the present paper we show that the X-boson method solves also the problem of the multiple roots of $N_{t}(\mu)$ that appear in the CHA.Comment: 13 pages, 6 figures e-mails: [email protected], [email protected], [email protected]

Cumulant Expansion Of The Periodic Anderson Model: General Derivation

We extend to the periodic Anderson model (PAM) the diagrammatic expansion in cumulants that was employed by Hubbard to study his model of a narrow band of strongly correlated electrons. The PAM is a lattice of localized and strongly correlated electrons with spin one-half and without orbital degeneracy, hybridized with a wide band of uncorrelated conduction electrons. We have extended the model by considering localized electronic states with an arbitrary scheme of energy levels: this extension would be useful to study intermediate valence compounds of Eu or Tm with the present formalism. We give the rules for the diagrammatic calculation of the grand canonical potential and of the Greens functions for the general model: only connected diagrams appear in those calculations and the lattice sums are unrestricted. To generate the cumulant averages it was necessary to employ external fields that are Grassman variables. We have found a simple way to extend the diagrammatic rules to the 0 case. The absence of excluded site restrictions, that leads to complicated excluded volume problems in other treatments, and the existence of linked cluster expansions, are features of the cumulant expansion. As an application of the present method, we have calculated the occupation numbers of localized and conduction electrons for the PAM in the limit of infinite Coulomb repulsion (U). © 1994 The American Physical Society.5024179331795

Heavy fermion d-wave superconductivity: a X-boson approach

From an extension of the periodic Anderson model (PAM) in the $U=\infty$ limit taking into account the effect of a nearest neighbor attractive interaction between $f$-electrons, we compare the obtained superconducting phase diagram of a two dimensional d-wave superconductor with the results obtained for an isotropic s-wave superconductor employing the X-boson method.Comment: Submitted to the Proceeding of the ICM 2003-Rome. Requires elsart3.cl

X-boson Cumulant Approach To The Topological Kondo Insulators

In this work we present a generalization of our previous work of the X-boson approach to the periodic Anderson model (PAM), adequate to study a novel class of intermetallic 4f and 5f orbitals materials: the topological Kondo insulators, whose paradigmatic material is the compound SmB6. For simplicity, we consider a version of the PAM on a 2D square lattice, adequate to describe Ce-based compounds in two dimensions. The starting point of the model is the 4f - Ce ions orbitals, with J 5/2 multiplet, in the presence of spin-orbit coupling. Our technique works well for all of the parameters of the model and avoids the unwanted phase transitions of the slave boson mean field theory. We present a critical comparison of our results with those of the usual slave boson method, that has been intensively used to describe this class of materials. We also obtain a new valence first order transition which we attribute to the dependence of the hybridization.568DIB; Dirección de Investigación, Universidad Nacional de ColombiaColeman, P., (1984) Phys. Rev., 29 (6), p. 3035Dzero, M., Sun, K., Galitski, V., Coleman, P., (2010) Phys. Rev. Lett., 104 (10), p. 106408Dzero, M., Sun, K., Coleman, P., Galitski, V., (2012) Phys. Rev., 85 (4), p. 045130Alexandrov, V., Dzero, M., Coleman, P., (2013) Phys. Rev. Lett., 111 (22), p. 226403Tran, M.T., Takimoto, T., Kim, K.S., (2012) Phys. Rev., 85 (12), p. 125128Legner, M., Rueg, A., Sigrist, M., Phys. Rev., 89, p. 085110Werner, J., Assaad, F.F., (2013) Phys. Rev., 88 (3), p. 035113Franco, R., Figueira, M.S., Foglio, M.E., (2003) Phys. Rev., 66 (4), p. 045112Steglich, F., Geibel, C., Gloss, K., Olesch, G., Schank, C., Wassilew, C., Loidl, A., Stewart, G.F., (1994) J. Low Temperature Phys., 95 (1-2), p. 3Derr, J., Knebel, G., Lapertot, G., Salce, B., Measson, M.-A., Flouquet, J., (2006) J. Phys.: Condens. Matter, 18 (6), p. 2089Natoli, V.D., Cohen, H.M., Fornberg, B., (1996) J. Computacional Phys., 126 (1), p. 9

X-boson cumulant approach to the periodic Anderson model

The Periodic Anderson Model (PAM) can be studied in the infinite U limit by employing the Hubbard X operators to project out the unwanted states. We have already studied this problem employing the cumulant expansion with the hybridization as perturbation, but the probability conservation of the local states (completeness) is not usually satisfied when partial expansions like the Chain Approximation (CHA) are employed. Here we treat the problem by a technique inspired in the mean field approximation of Coleman's slave-bosons method, and we obtain a description that avoids the unwanted phase transition that appears in the mean-field slave-boson method both when the chemical potential is greater than the localized level Ef at low temperatures (T) and for all parameters at intermediate T.Comment: Submited to Physical Review B 14 pages, 17 eps figures inserted in the tex

Short-range antiferromagnetic correlations in Kondo insulators

We study the influence of short range antiferromagnetic correlations between local $f$-electrons on the transport and thermodynamic properties of Kondo insulators, as first proposed by Coqblin et al. for metallic heavy fermions. The inter-site magnetic correlations produce an effective bandwidth for the $f$-electrons. They are treated on the same footing as the local Kondo correlations such that two energy scales appear in our approach. We discuss the competition between these two scales on the physical properties.Comment: 13 pages, 13 figures. To be published in Physics Letters

Fano resonance in electronic transport through a quantum wire with a side-coupled quantum dot: X-boson treatment

The transport through a quantum wire with a side coupled quantum dot is studied. We use the X-boson treatment for the Anderson single impurity model in the limit of $U=\infty$. The conductance presents a minimum for values of T=0 in the crossover from mixed-valence to Kondo regime due to a destructive interference between the ballistic channel associated with the quantum wire and the quantum dot channel. We obtain the experimentally studied Fano behavior of the resonance. The conductance as a function of temperature exhibits a logarithmic and universal behavior, that agrees with recent experimental results.Comment: 6 pages, 10 eps figs., revtex

Thermodynamic properties of the periodic Anderson model:X-boson treatment

We study the specific dependence of the periodic Anderson Model (PAM) in the limit of $U=\infty$ employing the X-boson treatment in two fifferent regimes of the PAM: the heavy fermion Kondo (HF-K) and the heavy fermion local magnetic regime (HF-LMM). We obtain a multiple peak structure for the specific heat in agreement with experimental results as well as the increase of the electronic effective mass at low temperatures associated with the HF-K regime. The entropy per site at low T tends to zero in the HF-K regime, corresponding to a singlet ground state, and it tends to $k_{B}ln(2)$ in the HF-LMM, corresponding to a doublet ground state at each site. The linear coefficient $\gamma(T)=C_{v}/T$ of the specific heat qualitatively agrees with the experimental results obtained for differents materials in the two regimes considered here.Comment: 9 pages, 14 figure

Elastic Scattering and Total Reaction Cross Section for the 6He + 27Al System

The elastic scattering of the radioactive halo nucleus 6He on 27Al target was measured at four energies close to the Coulomb barrier using the RIBRAS (Radioactive Ion Beams in Brazil) facility. The Sao Paulo Potential(SPP) was used and its diffuseness and imaginary strength were adjusted to fit the elastic scattering angular distributions. Reaction cross-sections were extracted from the optical model fits. The reduced reaction cross-sections of 6He on 27Al are similar to those for stable, weakly bound projectiles as {6,7}Li, 9Be and larger than stable, tightly bound projectile as 16O on 27Al.Comment: 7 pages, 1 table, 3 figure

Sub- and above barrier fusion of loosely bound 6^6Li with 28^{28}Si

Fusion excitation functions are measured for the system $^6$Li+$^{28}$Si using the characteristic $\gamma$-ray method, encompassing both the sub-barrier and above barrier regions, viz., $E_{lab}$= 7-24 MeV. Two separate experiments were performed, one for the above barrier region ($E_{lab}$= 11-24 MeV) and another for the below barrier region ($E_{lab}$= 7-10 MeV). The results were compared with our previously measured fusion cross section for the $^7$Li+$^{28}$Si system. We observed enhancement of fusion cross section at sub-barrier regions for both $^6$Li and $^7$Li, but yield was substantially larger for $^6$Li. However, for well above barrier regions, similar type of suppression was identified for both the systems.Comment: 8 pages, 6 figures, as accepted for publication in Eur.Phys.J.