Through density functional theory (DFT) calculations, we show that, in contrast to terrace sites of Pt(211) and Pt(111), on steplike sites of Pt(211) and Pt(110)-(2 x 1), methylene is more stable than methyl. The resulting site-dependent product selectivity for methane dissociation allows us to conciliate between theory and recent reflection absorption infrared spectroscopy (RAIRS) experiments, which might open a door to new applications of vicinal surfaces of Pt in heterogeneous catalysis and as templates for nanoscale patterning of self-assembled monolayers.

We report a combined experimental and theoretical study comparing methane dissociation on three different platinum surfaces Pt(111), Pt(211), and Pt(110)-(1 × 2). Reflection absorption infrared spectroscopy (RAIRS) was used to detect chemisorbed methyl species formed by dissociative chemisorption of CH 4 on specific surface sites and to measure surface-site-specific sticking coefficients of CH 4 on the terrace, step, and ridge sites as function of incident translational energy. Methane dissociation is observed to be direct on all sites and diffusion of the chemisorbed methyl species is absent for surface temperature below 150 K. The experimental data are compared with the results of density functional (DFT) calculations that give minimum energy barriers for CH 4 chemisorption that properly account for the experimental relative site-specific reactivities. Also in agreement with experiments, DFT results predict a negligible effect of co-adsorbed H and CH 3 species on the vibrational frequency of a methyl group chemisorbed on terrace and step sites of Pt(211). However, the origin of the red-shift of the RAIRS peak of CH 3 chemisorbed on terrace sites compared with that on step sites of Pt(211) remains elusive and still demands further investigation.

The electronic properties and spectroscopic features of a magnetic trimer with a Kondo-like coupling to a non-magnetic metallic substrate are analyzed at zero temperature. The substrate density of states is depressed in the trimer neighbourhood, being exactly zero at the substrate chemical potential. The size of the resonance strongly depends on the magnetic state of the trimer, and exhibits a two-state behavior. The geometrical dependence of these results agree qualitatively with recent experiments and could be reproduced in a triangular quantum dot arrangement.

Estudiamos el modelo de Hubbard de tres bandas como punto de partida para describir la estructura electrónica de los planos CuO2. Considerando a las interacciones que involucran a los orbitales de O dentro de la aproximación de Hartree-Fock, decimamos cuánticamente a dichos orbitales a fin de obtener un modelo efectivo para los orbitales de Cu. A posteriori, implementamos aproximaciones mediante la técnica de bosones esclavos para tratar la repulsión en los orbitales de Cu. En particular consideramos la transición metal-aislador que sufre este modelo, caracterizando los comportamientos correspondientes a aisladores de Mott y de transferencia de carga. La formulación que presentamos es original y permite el tratamiento de manera análoga a los estudios realizados en la literatura para el modelo de Hubbard de una banda.

Estudiamos el modelo de Hubbard extendido (MHE) con repulsión U en el sitio y V entre vecinos próximos, modificado por efectos de polarización considerados a segundo orden en teoría de perturbaciones. Este modelo es equivalente a un MHE con un U convenientemente renormalizado y que incluye además repulsión entre segundos vecinos. Usando un nuevo método basado en números topológicos (fases de Berry de carga y espín), generalizarnos a valores finitos del salto t el diagrama de fases en una dimensión obtenido por van den Brink et al. (Phys. Rev. Lett. 75, 4658 (1995)). El modelo presenta distintas fases en su estado fundamental (dos ondas de densidad de carga, una onda de densidad de espín y una fase intermedia con orden de espín y carga) dependiendo de los valores de los parámetros. La región ocupada por la fase intermedia disminuye para t creciente y desaparece para valores moderados.

Going beyond a recently proposed microscopic model [D. Mastrogiuseppe, A. Dobry, arXiv:0810.3018v1] for the incommensurate transition in the spin-Peierls TiOX (X=Cl, Br) compounds, in the present work we start by studying the thermodynamics of the model with XY spins and adiabatic phonons. We find that the system enters an incommensurate phase by a first order transition at a low temperature Tc1. At a higher temperature Tc2 a continuous transition to a uniform phase is found. Furthermore, we study the magnetism in the incommensurate phase by density matrix renormalization group (DMRG) calculations on a one-dimensional Heisenberg model where the exchange is modulated by the incommensurate atomic position pattern. When the wave vector q of the modulation is near π, we find local magnetized zones (LMZ) in which spins abandon their singlets as a result of the domain walls induced by the modulated distortion. When q moves far away enough from π, the LMZ disappear and the system develops incommensurate magnetic correlations induced by the structure. We discuss the relevance of this result regarding previous and future experiments in TiOCl.

We determine the quantum phase diagram of the one-dimensional Hubbard model with bond-charge interaction X in addition to the usual Coulomb repulsion U>0 at half-filling. For large enough X<t the model shows three phases. For large U the system is in the spin-density wave phase as in the usual Hubbard model. As U decreases, there is first a spin transition to a spontaneously dimerized bond-ordered wave phase and then a charge transition to a novel phase in which the dominant correlations at large distances correspond to an incommensurate singlet superconductor.

An Anderson impurity in a Hubbard model on chains with finite length is studied using the density-matrix renormalization group (DMRG) technique. In the first place, we analyzed how the reduction of electron density from half-filling to quarter-filling affects the Kondo resonance in the limit of Hubbard repulsion U=0. In general, a weak dependence with the electron density was found for the local density of states (LDOS) at the impurity except when the impurity, at half-filling, is close to a mixed valence regime. Next, in the central part of this paper, we studied the effects of finite Hubbard interaction on the chain at quarter-filling. Our main result is that this interaction drives the impurity into a more defined Kondo regime although accompanied in most cases by a reduction of the spectral weight of the impurity LDOS. Again, for the impurity in the mixed valence regime, we observed an interesting nonmonotonic behavior. We also concluded that the conductance, computed for a small finite bias applied to the leads, follows the behavior of the impurity LDOS, as in the case of non-interacting chains. Finally, we analyzed how the Hubbard interaction and the finite chain length affect the spin compensation cloud both at zero and at finite temperature, in this case using quantum Monte Carlo techniques.

We investigate the ground-state phase diagram of the Hubbard model for the AB(N-1) chain with filling 1/N, where N is the number of atoms per unit cell. In the strong-coupling limit, a charge transition takes place from a band insulator (BI) to a correlated insulator for increasing on-site repulsion U and positive on-site energy difference Delta (energy at A sites lower than at B sites). In the weak-coupling limit, a bosonization analysis suggests that for N > 2 the physics is qualitatively similar to the case N=2 which has already been studied: an intermediate phase emerges, which corresponds to a bond-ordered ferroelectric insulator (FI) with spontaneously broken inversion symmetry. We have determined the quantum phase diagram for the cases N=3 and N=4 from the crossings of energy levels of appropriate excited states, which correspond to jumps in the charge and spin Berry phases, and from the change of sign of the localization parameter z(L)(c). From these techniques we find that, quantitatively, the BI and FI phases are broader for N > 2 than when N=2, in agreement with the bosonization analysis. Calculations of the Drude weight and z(L)(c) indicate that the system is insulating for all parameters, with the possible exception of the boundary between the BI and FI phases.

A quantum dot coupled to ferromagnetically polarized one-dimensional leads is studied numerically using the density-matrix renormalization group method. Several real space properties and the local density of states at the dot are computed. It is shown that this local density of states is suppressed by the parallel polarization of the leads. In this case we are able to estimate the length of the Kondo cloud, and to relate its behavior to that suppression. Another important result of our study is that the tunnel magnetoresistance as a function of the quantum dot on-site energy is minimum and negative at the symmetric point.

The electronic properties and spectroscopic features of a magnetic trimer with a Kondo-like coupling to a non-magnetic metallic substrate are analyzed at zero temperature. The substrate density of states is depressed in the trimer neighbourhood, being exactly zero at the substrate chemical potential. The size of the resonance strongly depends on the magnetic state of the trimer, and exhibits a two-state behavior. The geometrical dependence of these results agree qualitatively with recent experiments and could be reproduced in a triangular quantum dot arrangement.

The zero-temperature magnetic field-dependent conductance of electrons through a one-dimensional non-interacting tight-binding chain with an interacting {\it side} dot is reviewed and analized further. When the number of electrons in the dot is odd, and the Kondo effect sets in at the impurity site, the conductance develops a wide minimum as a function of the gate voltage, being zero at the unitary limit. Application of a magnetic field progressively destroys the Kondo effect and, accordingly, the conductance develops pairs of dips separated by $U$, where $U$ is the repulsion between two electrons at the impurity site. Each one of the two dips in the conductance corresponds to a perfect spin polarized transmission, opening the possibility for an optimum spin filter. The results are discussed in terms of Fano resonances between two interfering transmission channels, applied to recent experimental results, and compared with results corresponding to the standard substitutional configuration, where the dot is at the central site of the non-interacting chain.

We compute the zero bias conductance of electrons through a single ballistic channel weakly coupled to a side quantum dot with Coulomb interaction. In contrast to the standard setup which is designed to measure the transport through the dot, the channel conductance reveals Coulomb blockade dips rather then peaks due to the Fano-like backscattering. At zero temperature the Kondo effect leads to the formation of broad valleys of small conductance corresponding to an odd number of electrons on the dot. By applying a magnetic field in the dot region we find two dips corresponding to a total suppression in the conductance of spins up and down separated by an energy of the order of the Coulomb interaction. This provides a possibility of a perfect spin filter.

We study the half-filled Hubbard chain including next-nearest-neighbor hopping t('). The model has three phases: one insulating phase with dominant spin-density-wave correlations at large distances (SDWI), another phase with dominant spin-dimer correlations or dimerized insulator (DI), and a third one in which long-distance correlations indicate singlet superconductivity (SS). The boundaries of the SDWI are accurately determined numerically through a crossing of excited energy levels equivalent to the jump in the spin Berry phase. The DI-SS boundary is studied using several indicators such as correlation exponent K-rho, Drude weight D-c, localization parameter z(L), and charge gap Delta(c).

The transmission of electrons through a noninteracting tight-binding chain with an interacting side quantum dot (QD) is analyzed. When the Kondo effect develops at the dot the conductance presents a wide minimum, reachingzero at the unitary limit. This result is compared to the opposite behavior found in an embedded QD. Application of a magnetic field destroys the Kondo effect and the conductance shows pairs of dips separated by the charging energy U. The results are discussed in terms of Fano antiresonances and explain qualitatively recent experimental results.

We obtain the quantum phase diagram of the Hubbard chain with alternating on-site energy at half filling. The model is relevant for the ferroelectric perovskites and organic mixed-stack donor-acceptor crystals. For any values of the parameters, the band insulator is separated from the Mott insulator by a dimer phase. The boundaries are determined accurately by crossing of excited levels with particular discrete symmetries. We show that these crossings coincide with jumps of charge and spin Berry phases with a clear geometrical meaning.

We consider a modified extended Hubbard model (EHM) which, in addition to the on-site repulsion U and nearest-neighbor repulsion V includes polarization effects in second-order perturbation theory. The model is equivalent to an EHM with renormalized U plus a next-nearest-neighbor repulsion term. Using a method based on topological quantum numbers (charge and spin Berry phases), we generalize to finite hopping t the quantum phase diagram in one dimension constructed by van den Brink et al. [Phys. Rev. Lett. 75, 4658 (1995)]. At hopping t = 0 there are two charge density-wave phases, one spin density-wave phase, and one intermediate phase with charge and spin ordering, depending on the parameter values. At t not equal 0 the nature of each phase is confirmed by studying correlation functions. However, in addition to the strong-coupling phases, a small region with bond ordering appears. The region occupied by the intermediate phase first increases and then decreases with increasing t, until it finally disappears for t of the order but larger than U. For small t, the topological transitions agree with the results of second-order perturbation theory.