Superconductivity in the Kondo lattice model

We study the Kondo lattice model with additional attractive interaction between the conduction electrons within the dynamical mean-field theory using the numerical renormalization group to solve the effective quantum impurity problem. In addition to normal-state and magnetic phases we also allow for the occurrence of a superconducting phase. In the normal phase we observe a very sensitive dependence of the low-energy scale on the conduction-electron interaction. We discuss the dependence of the superconducting transition on the interplay between attractive interaction and Kondo exchange.Comment: Submitted to ICM 2009 Conference Proceeding

Charge gaps and quasiparticle bands of the ionic Hubbard model

The ionic Hubbard model on a cubic lattice is investigated using analytical approximations and Wilson's renormalization group for the charge excitation spectrum. Near the Mott insulating regime, where the Hubbard repulsion starts to dominate all energies, the formation of correlated bands is described. The corresponding partial spectral weights and local densities of states show characteristic features, which compare well with a hybridized-band picture appropriate for the regime at small $U$, which at half-filling is known as a band insulator. In particular, a narrow charge gap is obtained at half-filling, and the distribution of spectral quasi-particle weight reflects the fundamental hybridization mechanism of the model

An Enhanced Perturbational Study on Spectral Properties of the Anderson Model

The infinite-$U$ single impurity Anderson model for rare earth alloys is examined with a new set of self-consistent coupled integral equations, which can be embedded in the large $N$ expansion scheme ($N$ is the local spin degeneracy). The finite temperature impurity density of states (DOS) and the spin-fluctuation spectra are calculated exactly up to the order $O(1/N^2)$. The presented conserving approximation goes well beyond the $1/N$-approximation ({\em NCA}) and maintains local Fermi-liquid properties down to very low temperatures. The position of the low lying Abrikosov-Suhl resonance (ASR) in the impurity DOS is in accordance with Friedel's sum rule. For $N=2$ its shift toward the chemical potential, compared to the {\em NCA}, can be traced back to the influence of the vertex corrections. The width and height of the ASR is governed by the universal low temperature energy scale $T_K$. Temperature and degeneracy $N$-dependence of the static magnetic susceptibility is found in excellent agreement with the Bethe-Ansatz results. Threshold exponents of the local propagators are discussed. Resonant level regime ($N=1$) and intermediate valence regime ($|\epsilon_f| <\Delta$) of the model are thoroughly investigated as a critical test of the quality of the approximation. Some applications to the Anderson lattice model are pointed out.Comment: 19 pages, ReVTeX, no figures. 17 Postscript figures available on the WWW at http://spy.fkp.physik.th-darmstadt.de/~frithjof

Conserving approximations in direct perturbation theory: new semianalytical impurity solvers and their application to general lattice problems

For the treatment of interacting electrons in crystal lattices approximations based on the picture of effective sites, coupled in a self-consistent fashion, have proven very useful. Particularly in the presence of strong local correlations, a local approach to the problem, combining a powerful method for the short ranged interactions with the lattice propagation part of the dynamics, determines the quality of results to a large extent. For a considerable time the non crossing approximation (NCA) in direct perturbation theory, an approach originally developed by Keiter for the Anderson impurity model, built a standard for the description of the local dynamics of interacting electrons. In the last couple of years exact methods like the numerical renormalization group (NRG) as pioneered by Wilson, have surpassed this approximation as regarding the description of the low energy regime. We present an improved approximation level of direct perturbation theory for finite Coulomb repulsion U, the crossing approximation one (CA1) and discuss its connections with other generalizations of NCA. CA1 incorporates all processes up to fourth order in the hybridization strength V in a self-consistent skeleton expansion, retaining the full energy dependence of the vertex functions. We reconstruct the local approach to the lattice problem from the point of view of cumulant perturbation theory in a very general way and discuss the proper use of impurity solvers for this purpose. Their reliability can be tested in applications to e.g. the Hubbard model and the Anderson-lattice model. We point out shortcomings of existing impurity solvers and improvements gained with CA1 in this context. This paper is dedicated to the memory of Hellmut Keiter.Comment: 45 pages, 22 figure

Field-induced phase transitions in a Kondo insulator

We study the magnetic-field effect on a Kondo insulator by exploiting the periodic Anderson model with the Zeeman term. The analysis using dynamical mean field theory combined with quantum Monte Carlo simulations determines the detailed phase diagram at finite temperatures. At low temperatures, the magnetic field drives the Kondo insulator to a transverse antiferromagnetic phase, which further enters a polarized metallic phase at higher fields. The antiferromagnetic transition temperature $T_c$ takes a maximum when the Zeeman energy is nearly equal to the quasi-particle gap. In the paramagnetic phase above $T_c$, we find that the electron mass gets largest around the field where the quasi-particle gap is closed. It is also shown that the induced moment of conduction electrons changes its direction from antiparallel to parallel to the field.Comment: 7 pages, 6 figure

Fast two-layer two-photon imaging of neuronal cell populations using an electrically tunable lens

Functional two-photon Ca2+-imaging is a versatile tool to study the dynamics of neuronal populations in brain slices and living animals. However, population imaging is typically restricted to a single two-dimensional image plane. By introducing an electrically tunable lens into the excitation path of a two-photon microscope we were able to realize fast axial focus shifts within 15 ms. The maximum axial scan range was 0.7 mm employing a 40x NA0.8 water immersion objective, plenty for typically required ranges of 0.2–0.3 mm. By combining the axial scanning method with 2D acousto-optic frame scanning and random-access scanning, we measured neuronal population activity of about 40 neurons across two imaging planes separated by 40 μm and achieved scan rates up to 20–30 Hz. The method presented is easily applicable and allows upgrading of existing two-photon microscopes for fast 3D scanning

The emergence of the unmarked: A new perspective on the language-specific function of Broca's Area

A number of neuroimaging studies have implicated an involvement of Broca's area, particularly of the pars opercularis of the left inferior frontal gyrus (IFG), in the processing of complex (permuted) sentences. However, functional interpretations of this region's role range from very general (e.g., in terms of working memory) to highly specific (e.g., as supporting particular types of syntactic operations). A dissociation of these competing accounts is often impossible because in most cases, the language internal complexity of permuted sentence structures is accompanied invariably by increasing costs of a more general cognitive nature (e.g., working memory, task difficulty, and acceptability). We used functional magnetic resonance imaging to explore the precise nature of the pars opercularis activation in the processing of permuted sentences by examining the permutation of pronouns in German. Although clearly involving a permutation operation, sentences with an initial object pronoun behave like simple, subject-initial sentences (e.g., in terms of acceptability) because of a rule stating that pronouns should generally precede non-pro-nominal arguments. The results of the experiment show that in contrast to non-pro-nominal permutations, sentences with a permuted pronoun do not engender enhanced pars opercularis activation. Our findings therefore speak against both language-related working memory and transformation-based accounts of this region's role in sentence comprehension. Rather, we argue that the pars opercularis of the left IFG supports the language-specific linearization of hierarchical linguistic dependencies

Low-energy properties of the Kondo lattice model

We study the zero-temperature properties of the Kondo lattice model within the dynamical mean-field theory. As impurity solver we use the numerical renormalization group. We present results for the paramagnetic case showing the anticipated heavy Fermion physics, including direct evidence for the appearance of a large Fermi surface for antiferromagnetic exchange interaction. Allowing for the formation of a Neel state, we observe at finite doping an antiferromagnetic metal below a critical exchange interaction, which shows a crossover from a local-moment antiferromagnet with a small Fermi surface for weak exchange coupling to a heavy-fermion antiferromagnet with a large Fermi surface for increasing exchange. Including lattice degrees of freedom via an additional Holstein term we observe a significant suppression of the Kondo effect, leading to strongly reduced lowenergy scale. For too large electron-phonon coupling we find a complete collaps of the heavy Fermi liquid and the formation of polarons.Comment: 11 pages, 7 figure

Inelastic Neutron scattering in CeSi_{2-x}Ga_x ferromagnetic Kondo lattice compounds

Inelastic neutron scattering investigation on ferromagnetic Kondo lattice compounds belonging to CeSi_{2-x}Ga_{x}, x = 0.7, 1.0 and 1.3, system is reported. The thermal evolution of the quasielastic response shows that the Kondo interactions dominate over the RKKY interactions with increase in Ga concentration from 0.7 to 1.3. This is related to the increase in k-f hybridization with increasing Ga concentration. The high energy response indicates the ground state to be split by crystal field in all three compounds. Using the experimental results we have calculated the crystal field parameters in all three compounds studied here.Comment: 12 Pages Revtex, 2 eps figures