Direct Coulomb Research Articles

Maximally Localized Wannier Orbitals and the Extended Hubbard Model for Twisted Bilayer Graphene

We develop an effective extended Hubbard model to describe the low-energy electronic properties of the twisted bilayer graphene. By using the Bloch states in the effective continuum model and with the aid of the maximally localized algorithm, we construct the Wannier orbitals and obtain an effective tight-binding model on the emergent honeycomb lattice. We found the Wannier state takes a peculiar three-peak form in which the amplitude maxima are located at the triangle corners surrounding the center. We estimate the direct Coulomb interaction and the exchange interaction between the Wannier states. At the filling of two electrons per super cell, in particular, we find an unexpected coincidence in the direct Coulomb energy between a charge-ordered state and a homogeneous state, which would possibly lead to an unconventional many-body state.

Distinct Electron Conductance Regimes in Bacterial Decaheme Cytochromes

AbstractShewanella oneidensis MR‐1 gains energy by extracellular electron transfer to solid surfaces. They employ c‐type cytochromes in two Mtr transmembrane complexes, forming a multiheme wire for electron transport across the cellular outer membrane. We investigated electron‐ and hole‐transfer mechanisms in the external terminal of the two complexes, MtrC and MtrF. Comparison of computed redox potentials with previous voltammetry experiments in distinct environments (isolated and electrode‐bound conditions of PFV or in vivo) suggests that these systems function in different regimes depending on the environment. Analysis of redox potential shifts in different regimes indicates strong coupling between the hemes via an interplay between direct Coulomb and indirect interactions through local structural reorganization. The latter results in the screening of Coulomb interactions and explains poor correlation of the strength of the heme‐to‐heme interactions with the distance between the hemes.

Distinct Electron Conductance Regimes in Bacterial Decaheme Cytochromes.

Shewanella oneidensis MR-1 gains energy by extracellular electron transfer to solid surfaces. They employ c-type cytochromes in two Mtr transmembrane complexes, forming a multiheme wire for electron transport across the cellular outer membrane. We investigated electron- and hole-transfer mechanisms in the external terminal of the two complexes, MtrC and MtrF. Comparison of computed redox potentials with previous voltammetry experiments in distinct environments (isolated and electrode-bound conditions of PFV or in vivo) suggests that these systems function in different regimes depending on the environment. Analysis of redox potential shifts in different regimes indicates strong coupling between the hemes via an interplay between direct Coulomb and indirect interactions through local structural reorganization. The latter results in the screening of Coulomb interactions and explains poor correlation of the strength of the heme-to-heme interactions with the distance between the hemes.

Condensation of Counterions Gives Rise to Contraction Transitions in a One-Dimensional Polyelectrolyte Gel.

The equilibrium volume of a polyelectrolyte gel results from a balance between the tendency to swell caused by outbound polymer/counterion diffusion along with Coulomb interactions on the one hand; and, on the other, the elastic resilience of the cross-linked polymer network. Direct Coulomb forces contribute both to non-ideality of the equilibrated Donnan osmotic pressure, but also to stretching of the network. To isolate the effect of polyelectrolyte expansion, we have analyzed a “one-dimensional” version of a gel, a linear chain of charged beads connected by Hooke’s law springs. As in the range of weak Coulomb strengths previously studied, the springs are significantly stretched by the repulsive interactions among the beads even when the Coulomb strength is strong enough to cause condensation of counterions. There is a quasi-abrupt transition from a stretched state to a partially collapsed state in a transition range between weak and strong Coulomb strengths. Fluctuations between stretched and contracted conformations occur within the transition range. As the solvent quality decreases past the transition range, a progressive collapse can result if the condensed counterions strengthen the spring constant.

Colloquium : Excitons in atomically thin transition metal dichalcogenides

Atomically thin materials such as graphene and monolayer transition metal dichalcogenides (TMDs) exhibit remarkable physical properties resulting from their reduced dimensionality and crystal symmetry. The family of semiconducting transition metal dichalcogenides is an especially promising platform for fundamental studies of two-dimensional (2D) systems, with potential applications in optoelectronics and valleytronics due to their direct band gap in the monolayer limit and highly efficient light-matter coupling. A crystal lattice with broken inversion symmetry combined with strong spin-orbit interactions leads to a unique combination of the spin and valley degrees of freedom. In addition, the 2D character of the monolayers and weak dielectric screening from the environment yield a significant enhancement of the Coulomb interaction. The resulting formation of bound electron-hole pairs, or excitons, dominates the optical and spin properties of the material. Here we review recent progress in our understanding of the excitonic properties in monolayer TMDs and lay out future challenges. We focus on the consequences of the strong direct and exchange Coulomb interaction, discuss exciton-light interaction and effects of other carriers and excitons on electron-hole pairs in TMDs. Finally, the impact on valley polarization is described and the tuning of the energies and polarization observed in applied electric and magnetic fields is summarized.

Sensitivity of electrospray molecular dynamics simulations to long-range Coulomb interaction models.

Molecular dynamics (MD) electrospray simulations of 1-ethyl-3-methylimidazolium tetrafluoroborate (EMIM-BF_{4}) ion liquid were performed with the goal of evaluating the influence of long-range Coulomb models on ion emission characteristics. The direct Coulomb (DC), shifted force Coulomb sum (SFCS), and particle-particle particle-mesh (PPPM) long-range Coulomb models were considered in this work. The DC method with a sufficiently large cutoff radius was found to be the most accurate approach for modeling electrosprays, but, it is computationally expensive. The Coulomb potential energy modeled by the DC method in combination with the radial electric fields were found to be necessary to generate the Taylor cone. The differences observed between the SFCS and the DC in terms of predicting the total ion emission suggest that the former should not be used in MD electrospray simulations. Furthermore, the common assumption of domain periodicity was observed to be detrimental to the accuracy of the capillary-based electrospray simulations.

Influence of the quantum dot geometry on p -shell transitions in differently charged quantum dots

Absorption spectra of neutral, negatively and positively charged semiconductor quantum dots are studied theoretically. We provide an overview of the main energetic structure around the p-shell transitions, including the influence of nearby nominally dark states. Based on the envelope function approximation, we treat the four-band Luttinger theory as well as the direct and short range exchange Coulomb interactions within a configuration interaction approach. The quantum dot confinement is approximated by an anisotropic harmonic potential. We present a detailed investigation of state mixing and correlations mediated by the individual interactions. Differences and similarities between the differently charged quantum dots are highlighted. Especially large differences between negatively and positively charged quantum dots become evident. We present a visualisation of energetic shifts and state mixtures due to changes in size, in-plane asymmetry and aspect ratio. Thereby we provide a better understanding of the experimentally hard to access question of quantum dot geometry effects in general. Our findings show a new method to determine the in-plane asymmetry from photoluminescense excitation spectra. Furthermore, we supply basic knowledge for tailoring the strength of certain state mixtures or the energetic order of particular excited states via changes in the shape of the quantum dot, which is highly interesting e.g. to understand relaxation paths.

Barrier to recombination of oppositely charged large polarons

Electronic charge carriers in ionic materials can self-trap to form large polarons. Interference between the ionic displacements associated with oppositely charged large polarons increases as they approach one another. Initially, this interference produces an attractive potential that fosters their merger. However, for small enough separations this interference generates a repulsive interaction between oppositely charged large polarons. In suitable circumstances, this repulsion can overwhelm their direct Coulomb attraction. Then, the resulting net repulsion between oppositely charged large polarons constitutes a potential barrier which impedes their recombination.

Plain s-Wave Superconductivity near Magnetic Criticality: Enhancement of Attractive Electron–Boson Coupling Vertex Corrections

Recent experiments revealed that the plain $s$-wave state without any sign-reversal emerges in various metals near the magnetic criticality. To understand this counter-intuitive phenomenon, we study the gap equation for the multiorbital Hubbard-Holstein model, by analyzing the vertex correction (VC) due to the higher-order electron-correlation effects. We find that the phonon-mediated orbital fluctuations are magnified by the VC for the susceptibility ($\chi$-VC). In addition, the charge-channel attractive interaction is enlarged by the VC for the coupling-constant ($U$-VC), which is significant when the interaction has prominent $q$-dependences so the Migdal theorem fails. Due to both $\chi$-VC and $U$-VC, the plain $s$-wave state is caused by the small electron-phonon interaction near the magnetic criticality against the repulsive Coulomb interaction. We find that the direct Coulomb repulsion for the plain $s$-wave Cooper pair is strongly reduced by the "multiorbital screening effect".

Resonant electronic excitation energy transfer by exchange mechanism in the quantum dot system

A microscopic theory of nonradiative resonance energy transfer between spherical A3B5 semiconductor quantum dots by the exchange mechanism is suggested. The interdot Coulomb interaction is taken into consideration. It is assumed that the quantum dot-donor and the quantum dot-acceptor are made from the same A3B5 compound and are embedded in the matrix of another material that produces potential barriers for electrons and holes. The dependences of the energy transfer rate on the quantum-dot system parameters are found in the frame of the Kane model that provides the most adequate description of the real spectra of A3B5 semiconductors. The analytical treatment is carried out with using the density matrix method, which enabled us to perform an energy transfer analysis both in the weak-interaction approximation and in the strong-interaction approximation. The numerical calculations showed the saturation of the energy transfer rate at the distances between the donor and the acceptor approaching the contact one. The contributions of the exchange and direct Coulomb intractions can be of the same order at the small distances and can have the same value in the saturation range.

Comparison of several algorithms of the electric force calculation in particle plasma models

This work is devoted to plasma modelling using the technique of molecular dynamics. The crucial problem of most such models is the efficient calculation of electric force. This is usually solved by using the particle-in-cell (PIC) algorithm. However, PIC is an approximative algorithm as it underestimates the short-range interactions of charged particles. We propose a hybrid algorithm which adds these interactions to PIC. Then we include this algorithm in a set of algorithms which we test against each other in a two-dimensional collisionless magnetized plasma model. Besides our hybrid algorithm, this set includes two variants of pure PIC and the direct application of Coulomb's law. We compare particle forces, particle trajectories, total energy conservation and the speed of the algorithms. We find out that the hybrid algorithm can be a good replacement of direct Coulomb's law application (quite accurate and much faster). It is however probably unnecessary to use it in practical 2D models.

The Compressibility of pH‐Sensitive Microgels at the Oil–Water Interface: Higher Charge Leads to Less Repulsion

AbstractpH‐responsive microgels are unique stabilizers for stimuli‐sensitive emulsions that can be broken on demand by changing the pH value. However, recent experiments have indicated that electrostatic interactions play a different role to that in conventional Pickering emulsions. The influence of charges on the interactions between microgels at the oil–water interface is now described. Compression isotherms of microgels with different charge density and architecture were determined in a Langmuir trough, and counter‐intuitive results were obtained: Charged microgels can be compressed more easily than uncharged microgels. The compressibility of microgels is thus not determined by direct Coulomb repulsion. Instead, the different swelling of the microgels in the charged and the uncharged states is proposed to be the key parameter.

The Compressibility of pH‐Sensitive Microgels at the Oil–Water Interface: Higher Charge Leads to Less Repulsion

pH-responsive microgels are unique stabilizers for stimuli-sensitive emulsions that can be broken on demand by changing the pH value. However, recent experiments have indicated that electrostatic interactions play a different role to that in conventional Pickering emulsions. The influence of charges on the interactions between microgels at the oil-water interface is now described. Compression isotherms of microgels with different charge density and architecture were determined in a Langmuir trough, and counter-intuitive results were obtained: Charged microgels can be compressed more easily than uncharged microgels. The compressibility of microgels is thus not determined by direct Coulomb repulsion. Instead, the different swelling of the microgels in the charged and the uncharged states is proposed to be the key parameter.

Systematic analysis of spectroscopic characteristics of the lanthanide and actinide ions with the 4fN−15d and 5fN−16d electronic configurations in a free state

Systematic consideration of the spectroscopic properties of the fN−1d excited electronic configurations of the di-, tri- and tetravalent lanthanide and actinide ions in a free state is presented. Variations of the Hartree–Fock calculated Slater parameters for the fN−1d electron configurations, spin–orbit (SO) interaction constant ζ for the f and d electrons, and averaged values of the second, fourth and sixth powers of the 4f, 5f, 5d, 6d electrons’ radial coordinate across both series were considered; functional dependencies between the mentioned quantities were obtained. It has been shown that the Coulomb interaction parameters F2(ff), F4(ff), and F6(ff) for the fN−1 core increase linearly with the atomic number Z, whereas the direct and exchange Coulomb parameters F2(fd), F4(fd), G1(fd), G3(fd), G5(fd) for the fN−1d configuration decrease linearly with Z. Since the SO interaction constant ζ1/4 is also proportional to Z, it was possible to find linear relationships between the Coulomb interaction parameters and SO constants for the f and d electrons, which effectively reduce the number of independent parameters in the free ion Hamiltonian. The constraining relations between the free ion Hamiltonian’s parameters obtained in the present paper can be used for simulations of the f–d transition spectra of these ions in various crystals.

Green's function for a spherical dielectric discontinuity and its application to simulation.

We present rapidly convergent expressions for the Green's function of the Poisson equation for spherically symmetric systems where the dielectric constant varies discontinuously in the radial direction. These expressions are used in Monte Carlo simulations of various electrolyte systems, and their efficiency is assessed. With only the leading term of the expansion included, a precision of the polarization energy of 0.01kJmol(-1) or better was achieved, which is smaller than the statistical uncertainty of a typical simulation. The inclusion of the dielectric inhomogeneity leads to a 2.5-fold increase of the computational effort, which is modest for this type of model. The simulations are performed on six types of systems having either (i) a uniform surface charge distribution, (ii) a uniform volume charge distribution, or (iii) mobile ions, which were neutralized by mobile counterions. The ion density distributions are investigated for different dielectric conditions. These spatial distributions are discussed in terms of the importance of (i) the direct mean-field Coulomb interaction, (ii) the surface charge polarization at the dielectric discontinuity, and/or (iii) the change in the attractive Coulomb correlations.

A study of proton breakup from exotic nuclei through various reaction mechanisms in 40A - 80AMeV energy range

We have studied the single proton breakup from weakly bound exotic nuclei due to several reaction mechanisms separately and their total and the interference effects, in order to clarify quantitatively which mechanism would dominate the measured observables. We have considered: (i) the recoil effect of the core-target Coulomb potential which we distinguish from the direct proton-target Coulomb potential, and (ii) nuclear breakup, which consists of stripping and diffraction. Thus, we have calculated the absolute values of breakup cross sections and parallel momentum distributions (LMD) for 8 B and 17 F projectiles on a light and a heavy target in a range of intermediate incident energies (40A-80A MeV) for each reaction mechanism. Furthermore the interference among the two Coulomb effects and nuclear diffraction has been studied in detail. The calculation of the direct and recoil Coulomb effects separately and of their interference is the new and most relevant aspect of this work.

Asymptotic expansion of two-electron integrals and its application to Coulomb and exchange lattice sums in metallic, semimetallic, and nonmetallic crystals

A simple, easily implemented, accurate, and efficient approximation of long-range electron-electron-repulsion and electron-nucleus-attraction integrals is proposed. It replaces each product of two atomic-orbital (AO) basis functions of an electron by a point charge centered at the midpoint of the two AO's. The magnitude of the point charge is equal to the overlap integral of the two AO's. Each integral is then rapidly evaluated in the direct algorithm as a Coulomb interaction between two point charges. This scheme is implemented in ab initio Hartree-Fock crystalline orbital theory and tested for one-, two-, and three-dimensional solids of metallic, semimetallic, and nonmetallic electronic structures, in which the lattice sums of the direct Coulomb and/or exchange interactions are expected to be slowly convergent. It is shown that this approximation reduces operation and/or memory costs by up to an order of magnitude to achieve converged lattice sums, although the scaling (size dependence) of operation cost is unchanged. An improved criterion for truncating the exchange lattice sum is also proposed.

Electronic Raman scattering and the Fano resonance in metallic carbon nanotubes

The Fano resonance spectra for the $G$ band in metallic carbon nanotubes are calculated as a function of laser excitation energy, in which the origin of the resonance is given by an interference between the continuous electronic Raman spectra and the discrete phonon spectra. We found that the second-order scattering process of the $\mathbf{q}\ensuremath{\ne}0$ electron-electron interaction is more relevant to the continuous spectra rather than the $\mathbf{q}=0$ first-order process because the $\mathbf{q}=0$ direct Coulomb interaction vanishes due to the symmetry of the two sublattices of a carbon nanotube.

Unimolecular Reactivity of the [Urea-Sr]2+Complex, a Metastable Dication in the Gas Phase: An Experimental and Theoretical Perspective

The interactions between urea and Sr(2+) in the gas phase have been investigated by combining electrospray ionization/mass spectrometry techniques and density functional and high-level ab initio molecular orbital calculations. Our theoretical survey indicates that [Sr(urea)](2+) adducts are thermodynamically stable with respect to direct Coulomb explosions. However, after isomerization, some of the local minima of the PES are thermodynamically unstable with respect to the formation of NH(4)(+), but kinetically metastable. The loss of neutral fragments with the concomitant generation of lighter doubly charged fragment ions, namely, [(H(3)N)Sr](2+) and [(HNCO)]Sr(2+), compete with the aforementioned Coulomb explosion processes yielding NH(4)(+) + [(NCO)Sr](+) and [(H(2)N)Sr](+) + [H(2)NCO](+), although the former processes dominate. Hence, both singly and doubly charged species are detected as dissociation products. Quite importantly, the observed eliminations of NH(3) or HNCO lead to the formation of new doubly charged species, which turn out to be thermodynamically stable.

Interplay of nuclear and Coulomb effects in proton breakup from exotic nuclei

This paper gives new insight to the study of dynamical effects in proton breakup as compared to neutron breakup from a weakly bound state in an exotic nucleus. Following our recent work [Ravinder Kumar and Angela Bonaccorso, Phys. Rev. C84 014613 (2011)] there has been some discussion in the literature [B. Paes, J. Lubiana, P.R.S. Gomes, V. Guimar\~aes, Nucl. Phys. A890 1 (2012); Y. Kucuk and A. M. Moro, Phys. Rev. C86 034601 (2012)], thus in order to clarify and asses quantitatively which mechanism would dominate measured observables, we study here several reaction mechanisms separately but also their total including interference. These mechanisms are: the recoil effect of the core-target Coulomb potential which we distinguish from the direct proton-target Coulomb potential and nuclear breakup, which consists of stripping and diffraction. Direct Coulomb breakup typically gives cross sections about an order of magnitude larger than the recoil term and the amount of nuclear diffraction vs. Coulomb depends on the target. Thus for each mechanism the absolute values of breakup cross sections and parallel momentum distributions for 8B and 17F projectiles calculated on a light and a heavy target in a range of intermediate incident energies (40-80A.MeV) are presented. Furthermore we study in detail the interference among the two Coulomb effects and nuclear diffraction. The calculation of the direct and recoil Coulomb effects separately and of their interference is the new and most relevant aspect of this paper.