Attractive Nearest-neighbor Interactions Research Articles

Phase separation andd-wave superconductivity in a two-dimensional extended Hubbard model with nearest-neighbor attractive interaction

Inhomogeneities on various length scales suggesting phase separation seem to be a generic feature of hole-doped high-temperature superconducting cuprates. Also firmly established is the d-wave symmetry of the superconducting state. The interplay of superconductivity and phase separation has been noted in previous mean-field studies of correlated electron models. To further explore this issue in a more rigorous approach we have conducted quantum Monte Carlo calculations of a two-dimensional Hubbard model with nearest-neighbor attractive interaction. For a vanishing on-site repulsion, the result agrees with that of Micnas, Ranninger, and Robaszkiewicz [Phys. Rev. B 39, 11 653 (1989)], and indicates that for a given strength of the attractive interaction, homogeneous d-wave superconducting phase can exist only above a critical doping concentration, below which phase separation occurs. A finite on-site repulsion modifies the phase separation behavior. A stronger d-wave pairing correlation is seen in the inhomogeneous phase compared to the homogeneous phase.

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

From an extension of the periodic Anderson model (PAM) in the U=∞ 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.

Heavy-fermion superconductivity: AnX-boson treatment

We use the X-boson method to study the heavy-fermion superconductivity phase, employing an extension of the periodic Anderson model in the $U=\ensuremath{\infty}$ limit with a nearest-neighbor attractive interaction between the localized f electrons. We show that higher values of the hybridization parameter imply lower values associated with the maximum of the superconducting critical temperature ${T}_{c},$ indicating that the real charge transfer between bands tends to destabilize the Cooper pairing. Moreover, we show that the superconductivity is constrained to the vicinity of a range of densities where the f-band density of states at the Fermi level ${\ensuremath{\rho}}_{f}(\ensuremath{\mu})$ has sufficiently high values, and it was found both for configurations where the system presents intermediate-valence and heavy-fermion behaviors, as experimentally observed. Finally, as the total occupation is raised and for large hybridization parameter V there is an insulator-superconductor transition, which is related to the existence of a hybridization gap that cannot be accessed by the slave-boson method, because when the chemical potential lies in or above the gap the system suffers the second-order phase transition characteristic of that method.

Phase Separation Due to Nearest Neighbor Attractive Interactions in a Two-Dimensional Model

We have studied a correlated fermion model with nearest neighbor attractive interactions on a square lattice by means of quantum Monte Carlo simulation. At half-filling this model exhibits rather strong correlation effects. Charge fluctuations are suppressed and the ground state is an insulator with long-range anitferromagnetic correlations. When doped with holes this model exihibits phase separation which seems to be triggered by the antiferromagnetic long-range correlations.

Critical and dynamical behavior of a driven diffusive lattice gas

In this work, a detailed analysis of the critical behavior of the Katz, Lebowitz, and Spohn (KLS) [Phys. Rev. B 28, 1665 (1983)] model is performed. This model considers a lattice gas of density ρ0 with nearest-neighbor attractive interactions between particles under the influence of an external driven field. The system is in contact with a reservoir at temperature T. The phase diagram of the KLS model is evaluated showing that it exhibits both first- and second-order phase transitions at different temperatures (Tc), depending on particle density. Ordered states are characterized by strips of high particle density running along the direction of the driving field, while disordered states exhibit gas-like behavior. A fit of the phase diagram (i.e., the Tc versus ρ0 curve) near the second-order transition is consistent with an order parameter critical exponent β≈0.33. This exponent is in agreement with an independent measurement performed by studying the dynamic evolution of the system. Furthermore, the strength of the first-order transitions is evaluated by measuring the relaxation of the system starting from both random (T→∞) configurations and well-ordered states (T→0), respectively.

Structure, bonding, and anharmonic librational motion of CO on Ir{100}

A combined low energy electron diffraction (LEED)—density functional theory (DFT) study of the structure of the Ir{100}-c(2×2)-CO phase provides a comparison of the two techniques for a simple molecular adsorbate. Both studies clearly identify atop adsorption and agree on the key structural parameters: a strong buckling of the first Ir layer, a short Ir–C bond length, and a slight lengthening of the CO bond. The molecule is found to be adsorbed in an upright configuration, although an incomplete treatment of the correlated vibrational motion of the CO molecule across the surface in the LEED analysis results in an apparent tilt of 8° from the surface normal. The DFT study determines a high adsorption energy of 2.65 eV for the c(2×2) phase which can be associated with the relief of the high tensile stress of the metastable Ir{100}-(1×1) phase and can be correlated with the short Ir–C bond. The 0.25 ML p(2×2)-CO phase displays an almost identical local bonding geometry but has a slightly lower adsorption energy of 2.61 eV, indicative of an attractive nearest neighbor interaction in the c(2×2) phase. The potential-energy surface for displacement of the CO molecule away from the atop position is found to display quartic anharmonicity. The resulting vibrational amplitude of 0.19 Å can be associated with a harmonic frequency of 8 meV, in good agreement with previous EELS measurement. The level of agreement between the LEED and DFT determined structures is sufficiently good to demonstrate that the two techniques are capable of converging on very similar structures. Furthermore, this study clearly demonstrates the future role for low-temperature LEED measurements and DFT studies in achieving an understanding of the structure, bonding, and energetics of molecules adsorbed at surfaces.

Scaling laws in adsorption on bivariate surfaces.

The adsorption of particles with nearest-neighbor attractive and repulsive interactions is studied through Monte Carlo simulation on bivariate surfaces characterized by patches of weak and strong adsorbing sites of size l. Patches are considered to have either a square or a strip geometry and they can be either arranged in a deterministic ordered structure or in a random way. Quantities are identified that scale obeying power laws as a function of the scale length l. The consequences of this finding are discussed for the determination of the energetic topography of the surface from adsorption measurements.

Nearest-neighbor attraction stabilizes staggered currents in the two-dimensional Hubbard model

Using a strong-coupling approach, we show that staggered current vorticity does not obtain in the repulsive two-dimensional Hubbard model for large on-site Coulomb interactions, as in the case of the copper oxide superconductors. This trend also persists even when nearest-neighbor repulsions are present. However, staggered flux ordering emerges when attractive nearest-neighbor Coulomb interactions are included. Such ordering opens a gap along the $(\ensuremath{\pi},0)\ensuremath{-}(0,\ensuremath{\pi})$ direction and persists over a reasonable range of doping.

Thermodynamics and diffusion of a lattice gas on a simple cubic lattice.

A lattice gas model with nearest neighbor attractive interactions on a simple cubic lattice is considered. The method of nonequilibrium statistical ensembles due to Zubarev is used to derive expressions for jump and chemical diffusion coefficients. For thermally activated hopping dynamics in the hydrodynamical (low frequency, long wavelength) limit, and neglecting specific memory effects, these expressions are represented in a simple form in terms of the zero concentration limit of the chemical diffusion coefficient and equilibrium characteristics, i.e., the chemical potential, and the probability for two nearest neighbor sites to be vacant. These equilibrium characteristics are calculated by means of the self-consistent diagram approximation. The equilibrium characteristics and diffusion coefficients are in a good agreement with extensive Monte Carlo simulation results.

Spin-density wave and superconductivity in an extended two-dimensional Hubbard model with nearest-neighbor attraction

We study the interplay of antiferromagnetic and superconducting orders in a two-dimensional Hubbard model with on-site repulsion and nearest-neighbor attractive interaction. This type of interaction has been widely used to model d-wave superconductivity. Our mean-field calculations indicate that such an attractive interaction enhances the staggered magnetization produced by the on-site repulsion. As a result, superconductivity is strongly suppressed. Stripe formation is also affected.

The diagram approximation for lattice systems

We suggest a new approximation for evaluating the thermodynamical and structural characteristics of lattice gases with attractive nearest neighbor interactions. Mean potentials, which nullify the two-vertex diagram contributions to the free energy diagram expansion, are introduced. The contribution of the lowest-order irreducible diagram with an adjustable parameter is taken into account. This parameter is determined from the requirement that the critical temperature coincides with its exact or best known value. The resulting expressions for the free energy, chemical potential and distribution functions are given in an analytical form. In spite of its simplicity, this approximation yields surprisingly accurate results for different types of two- and three-dimensional lattices.

Statistical–mechanical description of diffusion in interacting lattice gases

A Mori-type equation for the lattice concentration of an interacting lattice gas is constructed on the basis of the master equation in the framework of the nonequilibrium statistical ensemble method due to Zubarev. The general expression for the diffusion coefficient, which takes into account particle jumps of arbitrary length, spatial dispersion and memory effects is derived. In contrast to systems with reversible dynamics the relevant or quasiequilibrium distribution significantly contributes to the diffusion coefficient. This contribution is represented by two cofactors, namely the kinetic diffusion coefficient and the correlation function of concentration fluctuations. For lattice gases with thermally activated hopping dynamics in hydrodynamic (zero frequency and long wave) limit the former is reduced to Zhdanov's form that reflects an important role of equilibrium characteristics, i.e. the chemical potential and the two-site vacancy distribution function. The self-consistent diagram approximation is used to evaluate these characteristics for a two-dimensional lattice gas with nearest-neighbor attractive interaction on a square lattice. Results for the diffusion coefficient coincide within a few per cent with Monte-Carlo simulation data.

Lattice-gas transport at subcritical temperatures

Transport phenomena are considered in a lattice-gas system with attractive nearest neighbor interactions. When the temperature is lowered, the initially uniform adatom distribution is transformed to a mixture of two phases with different densities (first-order phase transition). The diffusion or transport coefficients describing the adatom flows in each phase are very different. We derive analytical expressions for the tracer and the jump diffusion coefficients of the whole system in the low-temperature region, when the concentrations of excessive adatoms in the dilute phase and vacancies in the dense phase can be treated as small parameters. Jump and tracer diffusion coefficients depend exponentially (as e 2 ϕ ) on the interaction parameter ϕ. Our finding is in agreement with results of a Monte Carlo (MC) study. The analytical solutions presented here cover the whole range of adatom concentrations from zero to full monolayer, describing single phases, the two-phase mixture and the phase transition regions in between. The agreement between theoretical results on MC data is good and shows the adequacy of our analytical approach. The theory is generalized to systems with an alternative jump mechanism and to 3D lattices.

Effect of Band Structure on the Symmetry of Superconducting States

Effects of band structure on the symmetry of superconducting (SC) states are studied. We show that various symmetries of SC states are possible within the same type of interaction when the shape of the Fermi surface is changed. As a simple model we consider a square lattice system with a nearest-neighbor attractive interaction, and find that the spin-triplet (( p x + i p y )-wave) and spin-singlet ( d - or s -wave) SC states, and states with their coexistence ( d + i p y , s + i p y ) can be stabilized if the electron density (and thus the Fermi surface) is changed. By taking into account the interlayer attractive interaction in this model, the stability of interlayer-pairing states with line nodes is examined, and its relation to the SC state of Sr 2 RuO 4 is discussed.

Diffusion studies in nonequilibrium systems with attractive interactions

Diffraction experiments can be used easily to measure the time evolution of a system under nonequilibrium conditions to attain a new equilibrium state and deduce ``nonequilibrium'' surface diffusion coefficients. It is not clear how the ``nonequilibrium'' diffusion coefficients extracted from such diffraction experiments should be interpreted. We study with Monte Carlo simulations the behavior of the ``nonequilibrium'' tracer and collective diffusion coefficients in a lattice-gas model with attractive nearest-neighbor interactions, as the system evolves in time from an initial random state to attain the $(1\ifmmode\times\else\texttimes\fi{}1)$ ordered state for temperatures ${T/T}_{c}<1.$ We calculate the dependence of the mean-square displacement $〈{R}^{2}〉$ on time and the collective diffusion from the relaxation of the nonequilibrium structure factor $S(\stackrel{\ensuremath{\rightarrow}}{q},t)$ within time sub-intervals under the assumption that quasiequilibrium holds. We determine the time-dependent ``nonequilibrium'' diffusion coefficients and extract the time-dependent activation energies. For both diffusion coefficients the ``nonequilibrium'' values obtained at late times are compared to the corresponding values obtained at equilibrium.

Interplay of superconductivity and magnetism in strong coupling

A model is introduced describing the interplay between superconductivity and spin-ordering. It is characterized by on-site repulsive electron-electron interactions, causing antiferromagnetism, and nearest-neighbor attractive interactions, giving rise to d-wave superconductivity. Due to a special choice for the lattice, this model has a strong-coupling limit where the superconductivity can be described by a bosonic theory, similar to the strongly coupled negative U Hubbard model. This limit is analyzed in the present paper. A rich mean-field phase diagram is found and the leading quantum corrections to the mean-field results are calculated. The first-order line between the antiferromagnetic- and the superconducting phase is found to terminate at a tricritical point, where two second-order lines originate. At these lines, the system undergoes a transition to- and from a phase exhibiting both antiferromagnetic order and superconductivity. At finite temperatures above the spin-disordering line, quantum-critical behavior is found. For specific values of the model parameters, it is possible to obtain SO(5) symmetry involving the spin- and the phase-sector at the tricritical point. Although this symmetry is explicitly broken by the projection to the lower Hubbard band, it survives on the mean-field level, and modes related to a spontaneously broken SO(5) symmetry are present on the level of the random phase approximation in the superconducting phase.

Stationary state in a two-temperature model with competing dynamics

A two-dimensional half-filled lattice gas model with nearest-neighbor attractive interaction is studied where particles are coupled to two thermal baths at different temperatures T1 and T2. The hopping of particles is governed by the heat bath at temperature T1 with probability p and the other heat bath (T2) with probability 1-p independently of the hopping direction. On a square lattice the vertical and horizontal interfaces become unstable while interfaces are stable in the diagonal directions. As a consequence, particles condense into a tilted square in the novel ordered state. The p dependence of the resulting nonequilibrium stationary state is studied by a Monte Carlo simulation and dynamical mean-field approximation as well.

Computer simulation of relaxation phenomena in star-branched polymers. Temperature dependence

Dynamic Monte Carlo simulations of simple models of star-branched polymers were conducted. A model star macromolecule consisted of f = arms of equal length with a total number of polymer segments up to 800. The chain was confined to a simple cubic lattice with simple nearest neighbor attractive interactions. The relaxation phenomena were studied by means of autocorrelation functions in wide ranges of temperatures. Short-time-scale dynamic processes in the entire star-branched chain were examined. It was found that under good solvent conditions the longest relaxation time of the end-to-center vector decreases with decreasing temperature. For low temperatures (below the Θ-point) where the chain is collapsed, the dependence of the relaxation time on the temperature is opposite.

Temperature dependance of properties of star-branched polymers: A computer simulation study

Dynamic Monte Carlo simulations of single star-branched polymer models were made. Star macromolecules were confined to a simple cubic lattice with the nearest-neighbor attractive interactions. Every star consisted of f=3 arms of equal length. Length of a star varied between 49 and 799 statistical segments. Static and dynamic properties of model stars were calculated in good solvent conditions, Θ-state and in the collapsed state. Change of the chain dimensions, diffusion coefficients, and their scaling exponents with the temperature was shown and discussed. The locations of the Θ temperature and the collapse transition temperature TC were estimated for all chain lengths under consideration. The differences in motion of inner and outer parts of a star-branched polymer in different solvent conditions were described. The existence of a high-density core in the center of star macromolecules was confirmed and the influence of the temperature on its magnitude was studied. An analysis of motion of different parts of star polymers and of the number of inter- and intra-armal contracts was performed.

Thermodynamically self-consistent theory of structure for three-dimensional lattice gases

Recently, methods were developed to solve with high accuracy the equations that describe a thermodynamically self-consistent theory for the two-body correlation function, and preliminary results were reported for three-dimensional lattice gases with nearest-neighbor attractive interaction [R. Dickman and G. Stell, Phys. Rev. Lett. 77, 996 (1996)]. Here we give a detailed description of our methods and of the results, which are found to be remarkably accurate for both the thermodynamics and structure of these systems. In particular, critical temperatures are predicted to within 0.2% of the best estimates from series expansions. Although above the critical temperature the theory yields the same critical exponents as the spherical model, this asymptotic behavior sets in only in a very narrow region around the critical point, so that the apparent exponents and the thermodynamics are well reproduced up to reduced temperatures of around ${10}^{\ensuremath{-}2}$. On the coexistence curve, on the other hand, the exponents are nonspherical, and considerably more accurate than the spherical ones. For instance, the exponent ${\ensuremath{\beta}}_{\mathrm{coex}}$ predicted by the theory for the shape of the coexistence curve is ${\ensuremath{\beta}}_{\mathrm{coex}}=0.35$.