The Cumulant Expansion for the Anderson Lattice with Finite U: The Completeness Problem

``Completeness'' (i.e. probability conservation) is not usually satisfied in the cumulant expansion of the Anderson lattice when a reduced state space is employed for $U\to \infty$. To understand this result, the well known ``Chain'' approximation is first calculated for finite $U$, followed by taking $U\to \infty$. Completeness is recovered by this procedure, but this result hides a serious inconsistency that causes completeness failure in the reduced space calculation. Completeness is satisfied and the inconsistency is removed by choosing an adequate family of diagrams. The main result of this work is that using a reduced space of relevant states is as good as using the whole space.Comment: Latex 22 pages, 6 figures with postscript files attached, accepted for publication in the Int. J. of Mod. Phys. B (1998). Subject field : Strongly Correlated System

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

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

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

Bulk Cr tips for scanning tunneling microscopy and spin-polarized scanning tunneling microscopy

A simple, reliable method for preparation of bulk Cr tips for Scanning Tunneling Microscopy (STM) is proposed and its potentialities in performing high-quality and high-resolution STM and Spin Polarized-STM (SP-STM) are investigated. Cr tips show atomic resolution on ordered surfaces. Contrary to what happens with conventional W tips, rest atoms of the Si(111)-7x7 reconstruction can be routinely observed, probably due to a different electronic structure of the tip apex. SP-STM measurements of the Cr(001) surface showing magnetic contrast are reported. Our results reveal that the peculiar properties of these tips can be suited in a number of STM experimental situations

The periodic Anderson model from the atomic limit and FeSi

The exact Green's functions of the periodic Anderson model for $U\to \infty$ are formally expressed within the cumulant expansion in terms of an effective cumulant. Here we resort to a calculation in which this quantity is approximated by the value it takes for the exactly soluble atomic limit of the same model. In the Kondo region a spectral density is obtained that shows near the Fermi surface a structure with the properties of the Kondo peak. Approximate expressions are obtained for the static conductivity $$ and magnetic susceptibility $\chi (T)$ of the PAM, and they are employed to fit the experimental values of FeSi, a compound that behaves like a Kondo insulator with both quantities vanishing rapidly for $T\to 0$. Assuming that the system is in the intermediate valence region, it was possible to find good agreement between theory and experiment for these two properties by employing the same set of parameters. It is shown that in the present model the hybridization is responsible for the relaxation mechanism of the conduction electrons.Comment: 26 pages and 8 figure