Bare Coulomb Interactions Research Articles

Yukawa potential for realistic prediction of Hubbard and Hund interaction parameters for transition metals

The generalized Hubbard model is an important theoretical model for modeling strongly correlated materials. To be able to theoretically predict the properties of the materials, the model requires Hubbard’s U and Hund’s J parameter that represent the on-site Coulomb and exchange interaction, respectively. For bare Coulomb interactions, the analytic expression of U and J are analytically described by Racah’s A,B,C parameters. However, the values of U are too large for transition-metal-based materials. To obtain more accurate values for realistic materials, we employ a Yukawa-type screened Coulomb interaction, characterized by screening constant λ. We characterize λ for transition metals. The modified A,B,C parameters give a more realistic U and J values.

Three-body interactions in generic fractional quantum Hall systems and impact of Galilean invariance breaking

We derive full analytic expressions of three-body interactions from Landau-level (LL) mixing in fractional quantum Hall systems with Schrieffer-Wolff transformation. The formalism can be applied to any LL, and to very general systems without rotational or Galilean invariance. We illustrate how three-body pseudopotentials can be readily computed from the analytical expressions for a wide variety of different systems, and show that for realistic systems, softening the bare Coulomb interactions (e.g., finite thickness or screening) can significantly suppress three-body interactions. More interestingly, for experimental systems without Galilean invariance (which is common for real materials), there is strong evidence that higher orders in band dispersion can drive the Moore-Read state from anti-Pfaffian to Pfaffian phase. Our analysis points to the importance of the realistic band structure details to the non-Abelian topological phases, and the analytical expressions we derived can also be very useful for high fidelity numerical computations.

Coulomb interactions and screening effects in few-layer black phosphorus: a tight-binding consideration beyond the long-wavelength limit

Coulomb interaction and its screening play an important role in many physical phenomena of materials ranging from optical properties to many-body effects including superconductivity. Here, we report on a systematic study of dielectric screening in few-layer black phosphorus (BP), a two-dimensional material with promising electronic and optical characteristics. We use a combination of a tight-binding model and rigorously determined bare Coulomb interactions, which allows us to consider relevant microscopic effects beyond the long-wavelength limit. We calculate the dielectric function of few-layer BP in the random phase approximation and show that it exhibits strongly anisotropic behavior even in the static limit. We also estimate the strength of effective local and non-local Coulomb interactions and determine their doping dependence. We find that the pz states responsible for low-energy excitations in BP provide a moderate contribution to the screening, weakening the on-site Coulomb interaction by less that a factor of two. Finally, we calculate the full plasmon spectrum of few-layer BP and discuss the effects beyond long-wavelengths.

Monte Carlo simulation of the tight-binding model of graphene with partially screened Coulomb interactions

We report on Hybrid-Monte-Carlo simulations of the tight-binding model with long-range Coulomb interactions for the electronic properties of graphene. We investigate the spontaneous breaking of sublattice symmetry corresponding to a transition from the semimetal to an antiferromagnetic insulating phase. Our short-range interactions thereby include the partial screening due to electrons in higher energy states from ab initio calculations based on the constrained random phase approximation [T.O.Wehling {\it et al.}, Phys.Rev.Lett.{\bf 106}, 236805 (2011)]. In contrast to a similar previous Monte-Carlo study [M.V.Ulybyshev {\it et al.}, Phys.Rev.Lett.{\bf 111}, 056801 (2013)] we also include a phenomenological model which describes the transition to the unscreened bare Coulomb interactions of graphene at half filling in the long-wavelength limit. Our results show, however, that the critical coupling for the antiferromagnetic Mott transition is largely insensitive to the strength of these long-range Coulomb tails. They hence confirm the prediction that suspended graphene remains in the semimetal phase when a realistic static screening of the Coulomb interactions is included.

Attractive forces in microporous carbon electrodes for capacitive deionization

The recently developed modified Donnan (mD) model provides a simple and useful description of the electrical double layer in microporous carbon electrodes, suitable for incorporation in porous electrode theory. By postulating an attractive excess chemical potential for each ion in the micropores that is inversely proportional to the total ion concentration, we show that experimental data for capacitive deionization (CDI) can be accurately predicted over a wide range of applied voltages and salt concentrations. Since the ion spacing and Bjerrum length are each comparable to the micropore size (few nanometers), we postulate that the attraction results from fluctuating bare Coulomb interactions between individual ions and the metallic pore surfaces (image forces) that are not captured by mean-field theories, such as the Poisson-Boltzmann-Stern model or its mathematical limit for overlapping double layers, the Donnan model. Using reasonable estimates of the micropore permittivity and mean size (and no other fitting parameters), we propose a simple theory that predicts the attractive chemical potential inferred from experiments. As additional evidence for attractive forces, we present data for salt adsorption in uncharged microporous carbons, also predicted by the theory.

Effect of nonhomogenous dielectric background on the plasmon modes in graphene double-layer structures at finite temperatures

We have calculated the plasmon modes in graphene double layer structures at finite temperatures, taking into account the inhomogeneity of the dielectric background of the system. The effective dielectric function is obtained from the solution of the Poisson equation of three-layer dielectric medium with the graphene sheets located at the interfaces, separating the different materials. Due to the momentum dispersion of the effective dielectric function, the intra- and inter-layer bare Coulomb interactions in the graphene double layer system acquires an additional momentum dependence--an effect that is of the order of the inter-layer interaction itself. We show that the energies of the in-phase and out-of-phase plasmon modes are determined largely by different values of the spatially dependent effective dielectric function. The effect of the dielectric inhomogeneity increases with temperature and even at high temperatures the energy shift induced by the dielectric inhomogeneity and temperature itself remains larger than the broadening of the plasmon energy dispersions due to the Landau damping. The obtained new features of the plasmon dispersions can be observed in frictional drag measurements and in inelastic light scattering and electron energy-loss spectroscopies.

Coulomb explosion in dicationic noble gas clusters: A genetic algorithm-based approach to critical size estimation for the suppression of Coulomb explosion and prediction of dissociation channels

We present a genetic algorithm based investigation of structural fragmentation in dicationic noble gas clusters, Ar(n)(+2), Kr(n)(+2), and Xe(n)(+2), where n denotes the size of the cluster. Dications are predicted to be stable above a threshold size of the cluster when positive charges are assumed to remain localized on two noble gas atoms and the Lennard-Jones potential along with bare Coulomb and ion-induced dipole interactions are taken into account for describing the potential energy surface. Our cutoff values are close to those obtained experimentally [P. Scheier and T. D. Mark, J. Chem. Phys. 11, 3056 (1987)] and theoretically [J. G. Gay and B. J. Berne, Phys. Rev. Lett. 49, 194 (1982)]. When the charges are allowed to be equally distributed over four noble gas atoms in the cluster and the nonpolarization interaction terms are allowed to remain unchanged, our method successfully identifies the size threshold for stability as well as the nature of the channels of dissociation as function of cluster size. In Ar(n)(2+), for example, fissionlike fragmentation is predicted for n=55 while for n=43, the predicted outcome is nonfission fragmentation in complete agreement with earlier work [Golberg et al., J. Chem. Phys. 100, 8277 (1994)].

Stability of Sarma phases in density imbalanced electron-hole bilayer systems

We study excitonic condensation in an electron-hole bilayer system with unequal layer densities at zero temperature. Using mean-field theory we solve the BCS gap equations numerically and investigate the effects of intra-layer interactions. We analyze the stability of the Sarma phase with $\bk,-\bk$ pairing by calculating the superfluid mass density and also by checking the compressibility matrix. We find that with bare Coulomb interactions the superfluid density is always positive in the Sarma phase, due to a peculiar momentum structure of the gap function originating from the singular behavior of the Coulomb potential at zero momentum and the presence of a sharp Fermi surface. Introducing a simple model for screening, we find that the superfluid density becomes negative in some regions of the phase diagram, corresponding to an instability towards a Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) type superfluid phase. Thus, intra-layer interaction and screening together can lead to a rich phase diagram in the BCS-BEC crossover regime in electron-hole bilayer systems.

Excitonic condensation in a double-layer graphene system

The possibility of excitonic condensation in a recently proposed electrically biased double-layer graphene system is studied theoretically. The main emphasis is put on obtaining a reliable analytical estimate for the transition temperature into the excitonic state. As in a double-layer graphene system the total number of fermionic ‘flavors’ is equal to N = 8 due to two projections of spin, two valleys and two layers, the large-N approximation appears to be especially suitable for theoretical investigation of the system. On the other hand, the large number of flavors makes screening of the bare Coulomb interactions very efficient, which, together with the suppression of backscattering in graphene, leads to an extremely low energy of the excitonic condensation. It is shown that the effect of screening on the excitonic pairing is just as strong in the excitonic state as it is in the normal state. As a result, the value of the excitonic gap Δ is found to be in full agreement with the previously obtained estimate for the mean-field transition temperature Tc, the maximum possible value Δmax, Tmaxc ∼ 10−7ϵF (ϵF is the Fermi energy) of both being in a 1mK range for a perfectly clean system. This proves that the energy scale ∼10−7ϵF really sets the upper bound for the transition temperature and invalidates the recently expressed conjecture about the high-temperature first-order transition into the excitonic state. These findings suggest that, unfortunately, the excitonic condensation in graphene double-layers can hardly be realized experimentally.

Electrostatic Interactions of Colloidal Particles at Vanishing Ionic Strength

Electrostatic interactions of colloidal particles are typically screened by mobile ions in the solvent. We measure the forces between isolated pairs of colloidal polymer microspheres as the density of bulk ions vanishes. The ionic strength is controlled by varying the concentration of surfactant (NaAOT) in a nonpolar solvent (hexadecane). While interactions are well-described by the familiar screened-Coulomb form at high surfactant concentrations, they are experimentally indistinguishable from bare Coulomb interactions at low surfactant concentration. Interactions are strongest just above the critical micelle concentration, where particles can obtain high surface potentials without significant screening, kappaa << 1. Exploiting the absence of significant charge renormalization, we are able to construct a simple thermodynamic model capturing the role of reverse micelles in charging the particle surface. These measurements provide novel access to electrostatic forces in the limit where the particle size is much less than the screening length, which is relevant not just to the nonpolar suspensions described here, but also to aqueous suspensions of nanoparticles.

Charge-Induced Conformational Changes of Dendrimers

We study the effect of chargeable monomers on the conformation of dendrimers of low generation by computer simulations, employing bare Coulomb interactions. The presence of the latter leads to an increase in size of the dendrimer due to a combined effect of electrostatic repulsion and the presence of counterions within the dendrimer, and also enhances a shell-like structure for the monomers of different generations. In the resulting structures the bond-length between monomers, especially near the center, will increase to facilitate a more effective usage of space in the outer-regions of the dendrimer.

Gas-liquid phase separation in oppositely charged colloids: Stability and interfacial tension

We study the phase behavior and the interfacial tension of the screened Coulomb (Yukawa) restricted primitive model (YRPM) of oppositely charged hard spheres with diameter sigma using Monte Carlo simulations. We determine the gas-liquid and gas-solid phase transitions using free energy calculations and grand-canonical Monte Carlo simulations for varying inverse Debye screening length kappa. We find that the gas-liquid phase separation is stable for kappasigma<or=4, and that the critical temperature decreases upon increasing the screening of the interaction (decreasing the range of the interaction). In addition, we determine the gas-liquid interfacial tension using grand-canonical Monte Carlo simulations. The interfacial tension decreases upon increasing the range of the interaction. In particular, we find that simple scaling can be used to relate the interfacial tension of the YRPM to that of the restricted primitive model, where particles interact with bare Coulomb interactions.

Dependence of the cloud size on interactions for a trapped degenerate ultracold plasma

We consider an ultracold plasma that has bosonic ions, at zero temperature. Assuming that ions are trapped by a harmonic trap, we calculate the size of the cloud for both screened and bare Coulomb interactions. Our results indicate that if clouds containing around 10 4 ions are confined with a trapping frequency of 10 kHz, stable radius is 15 μm for a fully screened two-component plasma while the radius increases to 2 mm for a one component plasma.

Screening of Coulomb interactions in transition metals

We discuss different methods of calculation of the screened Coulomb interaction $U$ in transition metals and compare the constraint local-density approximation (LDA) with the GW approach. We clarify that they offer complementary methods of treating the screening and should serve for different purposes. In the GW method, the renormalization of bare on-site Coulomb interactions between 3d electrons occurs mainly through the screening by the same 3d electrons, treated in the random phase approximation (RPA). The basic difference of the constraint-LDA method is that it deals with the neutral processes, where the Coulomb interactions are additionally screened by the ``excited'' electron, since it continues to stay in the system. This is the main channel of screening by the itinerant ($4sp$) electrons, which is especially strong in the case of transition metals and missing in the GW approach, although the details of this screening may be affected by additional approximations, which typically supplement these two methods. The major drawback of the conventional constraint-LDA method is that it does not allow to treat the energy-dependence of $U$. We propose a promising approximation based on the combination of these two methods. First, we take into account the screening of Coulomb interactions in the 3d-electron-line bands located near the Fermi level by the states from the subspace being orthogonal to these bands, using the constraint-LDA methods. The obtained interactions are further renormalized within the bands near the Fermi level in RPA. This allows the energy-dependent screening by electrons near the Fermi level including the same 3d electrons.

Exchange contributions to the grand potential of a uniform electron gas at finite temperature

An approximation for the grand potential Ω( μ, T, V) of a uniform electron gas at finite temperature, based on a partial resummation of the many-body perturbation expansion, has been suggested by Rebei and Hitchon. Their sum of exchange contributions did not contain a T 2 ln T term in a low temperature expansion and seemed to remove unphysical behaviour usually associated with long range bare Coulomb interactions, without invoking correlation and screening effects. We find their conclusions to be incorrect.

Nonlocal gradient corrections to the exchange free energy of an inhomogeneous many-fermion system at finite temperature

A general exact result is derived for the coefficient B x ( n; T) which determines the first gradient correction to the leading exchange contribution to the free energy at finite temperature of a weakly inhomogeneous extended many fermion system having arbitrary two-body interactions. Explicit analytical results are given in the case of bare Coulomb interactions, and the case of statically screened Coulomb interactions is studied numerically. It is shown that nonanalytical structure leads to different limiting values of B x ( n; T) when the inverse screening length and the temperature are both small. Some implications for physical many-electron systems are discussed, including the reasons for discrepancies between the first principles and semiempirical gradient coefficients for atomic exchange energies.

Why are some oxides metallic, while most are insulating?

A large variety of undoped binary and ternary transition metal oxides, including formally divalent, trivalent and tetravalent metal cations, have been examined. These 76 compounds are classified as either “metals”, “insulators”, or having a “metal-to-insulator” transition. In an attempt to understand these variations, the Zaanen-Sawatzky-Allen framework was used in which each compound can be characterized by three parameters: the Coulomb correlation or disproportionation energy ( U′), the charge-transfer energy (Δ) and the bandwidth ( W). Assuming W is constant, we have calculated U′ and Δ using a simple ionic model, which includes only the gas phase ionization potentials and the bare electrostatic Coulomb interactions between the ions. With this model, the occurence of metallic conductivity is remarkably well accounted for in these oxides.

Ideal-space treatment of the e++H to Ps+H+process

A new quantum mechanical formalism, is considered for the e+-H system; it explicitly introduces into the scattering picture the positronium (Ps) formation and breakup channels. In its lowest-order form the scattering T matrix of the theory (T(1)) contains two terms. The first of these (TB) is the conventional first Born approximation, while the second (TS), involving a non-local potential, can be interpreted as a screening of of the bare Coulomb interactions. Numerical applications seem to indicate that the new theory is characterised by much faster convergence properties than more conventional quantum mechanical treatments. In particular, the presence of the new Ts term, in the T(1) approximation, leads to differential and total cross sections comparable with distorted-wave results of the literature.