Attractive Nearest-neighbor Interactions Research Articles

Application of Bogoliubov-de Gennes equations to vortices in Hubbard superconductors

ABSTRACTIn this work, the formation of d-wave superconducting magnetic vortex is studied within the Bogoliubov-de Gennes formalism and the generalized Hubbard model, which leads to 2N2 coupled self-consistent equations for a supercell of N×N atoms. These equations determine the spatial variation of the superconducting gap as a function of the electron concentration and electron-electron interactions. The results show that the superconducting states induced by the correlated hopping (Δt3) are more sensitive to the presence of magnetic field than those induced by attractive nearest-neighbor interaction (V). Furthermore, we calculate the electronic specific heat as a function of the temperature for a given applied magnetic field, whose behavior has a qualitative agreement with experimental data.

Self-intermediate scattering function of strongly interacting three-dimensional lattice gases: time- and wave-vector-dependent tracer diffusion coefficient.

We investigate the self-intermediate scattering function (SISF) in a three-dimensional (3D) cubic lattice fluid (interacting lattice gas) with attractive nearest-neighbor interparticle interactions at a temperature slightly above the critical one by means of Monte Carlo simulations. A special representation of SISF as an exponent of the mean tracer diffusion coefficient multiplied by the geometrical factor and time is considered to highlight memory effects that are included in time and wave-vector dependence of the diffusion coefficient. An analytical expression for the diffusion coefficient is suggested to reproduce the simulation data. It is shown that the particles' mean-square displacement is equal to the time integral of the diffusion coefficient. We make a comparison with the previously considered 2D system on a square lattice. The main difference with the two-dimensional case is that the time dependence of particular characteristics of the tracer diffusion coefficient in the 3D case cannot be described by exponentially decreasing functions, but requires using stretched exponentials with rather small values of exponents, of the order of 0.2. The hydrodynamic values of the tracer diffusion coefficient (in the limit of large times and small wave vectors) defined through SIFS simulation results agree well with the results of its direct determination by the mean-square displacement of the particles in the entire range of concentrations and temperatures.

Monte Carlo tests of nucleation concepts in the lattice gas model

The conventional theory of homogeneous and heterogeneous nucleation in a supersaturated vapor is tested by Monte Carlo simulations of the lattice gas (Ising) model with nearest-neighbor attractive interactions on the simple cubic lattice. The theory considers the nucleation process as a slow (quasistatic) cluster (droplet) growth over a free energy barrier ΔF(*), constructed in terms of a balance of surface and bulk term of a critical droplet of radius R(*), implying that the rates of droplet growth and shrinking essentially balance each other for droplet radius R=R(*). For heterogeneous nucleation at surfaces, the barrier is reduced by a factor depending on the contact angle. Using the definition of physical clusters based on the Fortuin-Kasteleyn mapping, the time dependence of the cluster size distribution is studied for quenching experiments in the kinetic Ising model and the cluster size ℓ(*) where the cluster growth rate changes sign is estimated. These studies of nucleation kinetics are compared to studies where the relation between cluster size and supersaturation is estimated from equilibrium simulations of phase coexistence between droplet and vapor in the canonical ensemble. The chemical potential is estimated from a lattice version of the Widom particle insertion method. For large droplets it is shown that the physical clusters have a volume consistent with the estimates from the lever rule. Geometrical clusters (defined such that each site belonging to the cluster is occupied and has at least one occupied neighbor site) yield valid results only for temperatures less than 60% of the critical temperature, where the cluster shape is nonspherical. We show how the chemical potential can be used to numerically estimate ΔF(*) also for nonspherical cluster shapes.

Topological superfluid state of fermions on ap-band optical square lattice

In this paper we study an interacting mixture of ultracold spinless fermions on the $s$ band and bosons on the $p$ band in a 2D square optical lattice, of which the effective model is reduced to a $p$-band fermionic system with nearest-neighbor attractive interaction. From this effective $p$-band model, we find a translation symmetry protected ${\mathbb{Z}}_{2}$ topological superfluid that is characterized by a special fermion parity pattern at high-symmetry points in momentum space $\mathbf{k}=(0,0)$, $(0,\ensuremath{\pi})$, $(\ensuremath{\pi},0)$, $(\ensuremath{\pi},\ensuremath{\pi})$. Such ${\mathbb{Z}}_{2}$ topological superfluid supports the robust Majorana edge modes and a new type of low-energy excitation---(supersymmetric) ${\mathbb{Z}}_{2}$ link excitation.

Microscopic Derivation of Ginzburg–Landau Equations for Coexistent States of Superconductivity and Magnetism

Ginzburg-Landau (GL) equations for the coexistent states of superconductivity and magnetism are derived microscopically from the extended Hubbard model with on-site repulsive and nearest-neighbor attractive interactions. In the derived GL free energy a cubic term that couples the spin-singlet and spin-triplet components of superconducting order parameters (SCOP) with magnetization exists. This term gives rise to a spin-triplet SCOP near the interface between a spin-singlet superconductor and a ferromagnet, consistent with previous theoretical studies based on the Bogoliubov de Gennes method and the quasiclassical Green's function theory. In coexistent states of singlet superconductivity and antiferromagnetism it leads to the occurrence of pi-triplet SCOPs.

Thermodynamic theory of phase transitions in driven lattice gases

We formulate an approximate thermodynamic theory of the phase transition in driven lattice gases with attractive nearest-neighbor interactions. We construct the van der Waals equation of state for a driven system where a nonequilibrium chemical potential can be expressed as a function of density and driving field. A Maxwell's construction leads to the phase transition from a homogeneous fluid phase to the coexisting phases of gas and liquid.

Memory effects in strongly interacting lattice gases: Self-intermediate scattering function studies

We investigate in detail the self-intermediate scattering function (SISF) of a lattice fluid (interacting lattice gas) with attractive nearest-neighbor interparticle interactions at a temperature slightly above the critical one by means of Monte Carlo simulations. An analytical expression is suggested to reproduce the simulation data. This expression is the generalization of the hydrodynamic limit with the wave vector, the time-dependent tracer diffusion coefficient, and the lattice geometry factor, instead of the square of the wave vector. The tracer diffusion coefficient is given by its zero wave-vector limit multiplied by the exponent of a function that contains only one fitting parameter describing its wave-vector dependence. In order to represent the time dependence of the SISF and to understand the time scales of the lattice fluid relaxation processes, we use two- and three-exponential fitting functions. The relaxation times group in three well-separated regions around 10, 100, and 1000 Monte Carlo steps and show weak concentration dependence. The analytical expression can also be used to calculate the lattice fluid dynamical structure factor.

Competing pairing states for ultracold fermions in optical lattices with an artificial staggered magnetic field

We study fermionic superfluidity in an ultracold Bose-Fermi mixture loaded into a square optical lattice subjected to a staggered flux. While the bosons form a Bose-Einstein condensate at very low temperature and weak interaction, the interacting fermions experience an additional long-ranged attractive interaction mediated by phonons in the bosonic condensate. This leads us to consider a generalized Hubbard model with on-site and nearest-neighbor attractive interactions, which give rise to two competing pairing channels. We use the Bardeen-Cooper-Schrieffer theory to determine the regimes where distinct fermionic superfluids are stabilized and find that the nonlocal pairing channel favors a superfluid state which breaks both the gauge and the lattice symmetries, similar to unconventional superconductivity occurring in some strongly correlated systems. Furthermore, the particular structure of the single-particle spectrum leads to unexpected consequences, for example, a dome-shaped superfluid region in the temperature versus filing fraction phase diagram, with a normal phase that contains much richer physics than a Fermi liquid. Notably, the relevant temperature regime and coupling strength are readily accessible in state of the art experiments with ultracold trapped atoms.

Superconducting state with a finite-momentum pairing mechanism in zero external magnetic field

In the BCS theory of superconductivity, one assumes that all Cooper pairs have the same center-of-mass momentum. This is indeed enforced by self-consistency if the pairing interaction is momentum independent. Here, we show that for an attractive nearest-neighbor interaction, this is different. In this case, stable solutions with pairs with momenta $\mathbf{q}$ and $\ensuremath{-}\mathbf{q}$ coexist and, for a sufficiently strong interaction, one of these states becomes the ground state of the superconductor. The possibility for a finite-momentum pairing state emerges only for nodal superconductors and is accompanied by a charge order with wave vector $2\mathbf{q}$. For a weak pairing interaction, the ground state is a $d$-wave superconductor.

Negative diffusion coefficient in a two-dimensional lattice-gas system with attractive nearest-neighbor interactions

Collective diffusion in a two-dimensional lattice-gas system undergoing first-order phase transition is studied both theoretically and by means of Monte Carlo (MC) simulations. The nearest-neighbor attractive interactions result in the formation of a two-phase mixture in which the characteristic size of the dense phase grows with time as ${t}^{1/3}$. It is shown analytically that the evolution of large-scale coverage inhomogeneities is governed by the diffusion equation with a negative diffusion coefficient. Similar to the phenomenon of Ostwald ripening, the Gibbs-Thompson effect is responsible for this abnormal diffusion. MC simulations of random jumps of individual particles also show the presence of negative diffusion caused by the macroscopically inhomogeneous distribution of particle density. The collective diffusion coefficients obtained both theoretically and by means of MC simulations are in satisfactory agreement.

Interplay between spin-singlet and spin-triplet order parameters in a model of an anisotropic superconductor with cuprate planes

Model of a two-dimensional anisotropic superconductor with a relatively wide, partially filled conduction band is considered. Attractive nearest neighbor interaction with the amplitude V1, and on-site interaction (with the amplitude V0) taken either as repulsive or attractive are included in the model, along with the tight-binding dispersion relation implying singularities in the density of states. The analytic study is based on the conformal transformation method, which can be regarded as an extension of the Van Hove Scenario, plausible for anisotropic systems such as high-Tc cuprates. Employing the Fourier harmonics as a complete and orthogonal basis for irreducible representations of the cuprate plane symmetry group (C4v), the symmetry of the superconducting order parameter is identified for various values of the model parameters. A wide range of parameters η = 2t1/t0 (the ratio of the second and the first nearest neighbor hopping integrals) and n (the carrier concentration) is studied. The obtained diagrams allow one to identify and mark the areas of stability for the superconducting spin-singlet s- and d-wave and the spin-triplet p-wave order parameters. In particular the problem of coexistence of the s-, p- and d-wave order parameters is addressed and solved for selected values of the ratio V0/V1. A possible island of stability of the d-wave order parameter in the s-wave order parameter environment for a relatively strong on-site interaction is revealed. The triple points, around which the s-, d-, and p-wave order parameters coexist, are identified on the diagrams. It is shown that results of the calculations performed for the two-dimensional tight-binding band model are dissimilar with some obtained within the standard BCS-type approximation. The influence of the on-site interaction on the stability of the s-wave order parameter is explained in detail. The developed and widely illustrated formalism can be easily applied to some more composed models.

Dynamic behavior of the interface of striplike structures in driven lattice gases

In this work, the dynamic behavior of the interfaces in both the standard and random driven lattice gas models (DLG and RDLG, respectively) is investigated via numerical Monte Carlo simulations in two dimensions. These models consider a lattice gas of density rho=12 with nearest-neighbor attractive interactions between particles under the influence of an external driven field applied along one fixed direction in the case of the DLG model, and a randomly varying direction in the case of the RDLG model. The systems are also in contact with a reservoir at temperature T . Those systems undergo a second-order nonequilibrium phase transition between an ordered state characterized by high-density strips crossing the sample along the driving field, and a quasilattice gas disordered state. For T less, similarT_{c} , the average interface width of the strips (W) was measured as a function of the lattice size and the anisotropic shape factor. It was found that the saturation value W_{sat};{2} only depends on the lattice size parallel to the external field axis L_{y} and exhibits two distinct regimes: W_{sat};{2} proportional, variantlnL_{y} for low temperatures, that crosses over to W_{sat};{2} proportional, variantL_{y};{2alpha_{I}} near the critical zone, alpha_{I}=12 being the roughness exponent of the interface. By using the relationship alpha_{I}=1(1+Delta_{I}) , the anisotropic exponent for the interface of the DLG model was estimated, giving Delta_{I} approximately 1 , in agreement with the computed value for anisotropic bulk exponent Delta_{B} in a recently proposed theoretical approach. At the crossover region between both regimes, we observed indications of bulk criticality. The time evolution of W at T_{c} was also monitored and shows two growing stages: first one observes that W proportional, variantlnt for several decades, and in the following times one has W proportional, variantt;{beta_{I}} , where beta_{I} is the dynamic exponent of the interface width. By using this value we estimated the dynamic critical exponent of the correlation length in the perpendicular direction to the external field, giving z_{ perpendicular};{I} approximately 4 , which is consistent with the dynamic exponent of the bulk critical transition z_{ perpendicular};{B} in both theoretical approaches developed for the standard model. A similar scenario was also observed in the RDLG model, suggesting that both models may belong to the same universality class.

Islands of stability of the d-wave order parameter in s-wave anisotropic superconductors

In this paper we find and present on diagrams in the coordinates of η=2t1/t0 (the ratio of the second and the first nearest neighbor hopping integrals) and n (the carrier concentration) the areas of stability for the superconducting spin-singlet s- and d-wave and the spin-triplet p-wave order parameters hatching out during the phase transition from the normal to the superconducting phase. The diagrams are obtained for an anisotropic two-dimensional superconducting system with a relatively wide partially-filled conduction band. We study a tight-binding model with an attractive nearest neighbor interaction with the amplitude V1, and the on-site interaction (with the amplitude V0) taken either as repulsive or attractive. The problem of the coexistence of the s-, p- and d-wave order parameters is addressed and solved for chosen values of the ratio V0/V1. A possible island of stability of the d-wave order parameter in the s-wave order parameter environment for a relatively strong on-site interaction is revealed. The triple points, around which the s-, d-, and p-wave order parameters coexist, are localized on diagrams. It is shown that results of the calculations performed for the two-dimensional tight-binding band model are dissimilar with some obtained within the BCS-type approximation.

Novel anisotropic superconductivity in nano-structured superconductors

Using the Bogoliubov-de Gennes equation of a tight-binding electron model with attractive on-site and nearest-neighbor sites interactions, we investigate the superconducting structure of nano-structured anisotropic superconductors. Numerical results show that nano-scaled π/4-rotated square d-wave superconductors show various type of superconductivities depending on the size. Especially, s+id superconductivity, appears when size of superconductors is 10 times of coherence length.

INHOMOGENEOUS d-WAVE SUPERCONDUCTIVITY AND ANTIFERROMAGNETISM IN A TWO-DIMENSIONAL EXTENDED HUBBARD MODEL WITH NEAREST-NEIGHBOR ATTRACTIVE INTERACTION

To understand the interplay of d-wave superconductivity and antiferromagnetism, we consider a two-dimensional extended Hubbard model with nearest neighbor attractive interaction. The Hamiltonian is solved in the mean field approximation on a finite lattice. In the impurity-free case, the minimum energy solutions show phase separation as predicted previously based on free energy argument. The phase separation tendency implies that the system can be easily rendered inhomogeneous by a small external perturbation. Explicit solutions of a model including weak impurity potentials are indeed inhomogeneous in the spin-density-wave and d-wave pairing order parameters. Relevance of the results to the inhomogeneous cuprate superconductors is discussed.

Kinetic Monte Carlo simulations of electrodeposition: Crossover from continuous to instantaneous homogeneous nucleation within Avrami’s law

The influence of lateral adsorbate diffusion on the dynamics of the first-order phase transition in a two-dimensional Ising lattice gas with attractive nearest-neighbor interactions is investigated by means of kinetic Monte Carlo simulations. For example, electrochemical underpotential deposition proceeds by this mechanism. One major difference from adsorption in vacuum surface science is that under control of the electrode potential and in the absence of mass-transport limitations, local adsorption equilibrium is approximately established. We analyze our results using the theory of Kolmogorov, Johnson and Mehl, and Avrami (KJMA), which we extend to an exponentially decaying nucleation rate. Such a decay may occur due to a suppression of nucleation around existing clusters in the presence of lateral adsorbate diffusion. Correlation functions prove the existence of such exclusion zones. By comparison with microscopic results for the nucleation rate I and the interface velocity of the growing clusters v, we can show that the KJMA theory yields the correct order of magnitude for Iv 2. This is true even though the spatial correlations mediated by diffusion are neglected. The decaying nucleation rate causes a gradual crossover from continuous to instantaneous nucleation, which is complete when the decay of the nucleation rate is very fast on the time scale of the phase transformation. Hence, instantaneous nucleation can be homogeneous, producing negative minima in the two-point correlation functions. We also present in this paper an n-fold way Monte Carlo algorithm for a square lattice gas with adsorption/desorption and lateral diffusion.

Conductance of quantum wires: A numerical study of effects of an impurity and interactions

We use the non-equilibrium Green's function formalism along with a self-consistent Hartree-Fock approximation to numerically study the effects of a single impurity and interactions between the electrons (with and without spin) on the conductance of a quantum wire. We study how the conductance varies with the wire length, the temperature, and the strength of the impurity and interactions. The dependence of the conductance on the wire length and temperature is found to be in rough agreement with the results obtained from a renormalization group analysis based on the Hartree-Fock approximation. For the spin-1/2 model with a repulsive on-site interaction or the spinless model with an attractive nearest neighbor interaction, we find that the conductance increases with increasing wire length or decreasing temperature. This can be qualitatively explained using the Born approximation in scattering theory. For a strong impurity, the conductance is significantly different for a repulsive and an attractive impurity; this is due to the existence of a bound state in the latter case. In general, the large density deviations at short distances have an appreciable effect on the conductance which is not captured by the renormalization group analysis.

INTERPLAY OF D-WAVE SUPERCONDUCTIVITY AND ANTIFERROMAGNETISM IN THE CUPRATE SUPERCONDUCTORS: PHASE SEPARATION AND THE PSEUDOGAP PHASE DIAGRAM

To understand the interplay of d-wave superconductivity and antiferromagnetism in the cuprates, we consider a two-dimensional extended Hubbard model with nearest neighbor attractive interaction. Free energy of the homogeneous (coexisting superconducting and antiferromagnetic) state calculated as a function of the band filling shows a region of phase separation. The phase separation caused by the intersite attractive force leads to novel insights into salient features of the pseudogap phase diagram. In particular, the upper crossover curve can be identified with the phase separation boundary. At zero temperature, the boundary constitutes a critical point. The inhomogeneity observed in the underdoped cuprates is a consequence of incomplete phase separation. The disorder (inhomogeneity) brings about the disparity between the high pseudogap temperature and the low bulk superconducting transition temperature.

Nonequilibrium effects in diffusion of interacting particles on vicinal surfaces

We study the influence of nonequilibrium conditions on the collective diffusion of interacting particles on vicinal surfaces. To this end, we perform Monte Carlo simulations of a lattice-gas model of an ideal stepped surface, where adatoms have nearest-neighbor attractive or repulsive interactions. Applying the Boltzmann-Matano method to spreading density profiles of the adatoms allows the definition of an effective, time-dependent collective diffusion coefficient D(C) (t)(theta) for all coverages theta. In the case of diffusion across the steps and strong binding at lower step edges we observe three stages in the behavior of the corresponding D(xx,C) (t)(theta). At early times when the adatoms have not yet crossed the steps, D(xx,C) (t)(theta) is influenced by the presence of steps only weakly. At intermediate times, where the adatoms have crossed several steps, there are sharp peaks at coverages theta<1L and theta>1-1L, where L is the terrace width. These peaks are due to different rates of relaxation of the density at successive terraces. At late stages of spreading, these peaks vanish and D(xx,C) (t)(theta) crosses over to its equilibrium value, where for strong step edge binding there is a maximum at theta=1L. In the case of diffusion in direction along the steps the nonequilibrium effects in D(yy,C) (t)(theta) are much weaker, and are apparent only when diffusion along ledges is strongly suppressed or enhanced.

Superconductor–insulator transition induced by pressure within the X-boson approach

The pressure induced superconducting phase diagram is calculated for 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 analyze the role of the chemical potential compared to several plots of the f-band density of states and we also found a superconductor–insulator transition induced by pressure when the chemical potential crosses the hybridization gap.