Long-range Coulomb Interaction Research Articles

Interatomic Coulombic electron capture beyond the virtual photon approximation.

Via the interatomic Coulombic electron capture (ICEC) process, an electron can be captured by an atom or a molecule, while the binding and excess energy is transferred, via a long-range Coulomb interaction, to a neighboring atom or molecule. The transferred energy can be used to ionize or electronically excite the neighboring species. When the two species are asymptotically far apart, an analytical formula for the ICEC cross sections can be derived. The latter can then be estimated using only the energies and the photoionization cross sections of each species. In this work, we develop an analytical model that allows us to predict the ICEC cross sections when the size of the involved species is comparable to the distance between the two entities. Using abinitio R-matrix results for various systems, we show that the new model reduces the error of the asymptotic formula by two orders of magnitude on average while only using parameters that can be taken from the properties of each species.

Effective Model Reduction Scheme for the Electronic Structure of Highly Doped Semiconducting Polymers.

Highly doped organic polymers have emerged as prominent candidates within novel technological disciplines, yet the fundamental correlation between structure and charge transport characteristics still remains missing. Toward this objective, an efficient model reduction scheme for highly doped polymer chains is developed considering the paradigmatic case of poly(3,4-ethylenedioxythiophene)-poly(styrenesulfonate) (PEDOT-PSS). The reduced model accounts for the chemical and structural details of the conducting polymer chain in addition to the long-range Coulombic interactions between charge carriers (holes) and dopant ions and the Coulombic repulsion between holes residing on the PEDOT chain. The model is shown to reproduce the intrachain hole-density profile of bulk polymer chains within a mean-field description. Furthermore, and critically, the model is adept at determining the energy distribution of doped PEDOT samples that in effect, influences the hole distribution among polymer chains. The hole distribution so obtained broadly upholds the approximation of a homogeneous charge-carrier distribution in doped polymers commonly found in the literature. In addition, it is observed that the spin configuration of the charge carriers dictates the energetics of the doped chains while it is a critical function of the chain length, carrier density, and disorder parameters.

Softening of the optical phonon by reduced interatomic bonding strength without depolarization.

Softening of the transverse optical (TO) phonon, which could trigger ferroelectric phase transition, can usually be achieved by enhancing the long-range Coulomb interaction over the short-range bonding force1, for example, by increasing the Born effective charges2. However, it suffers from depolarization effects3,4 as the induced ferroelectricity is suppressed on size reduction of the host materials towards high-density nanoscale electronics. Here, we present an alternative route to drive the TO phonon softening by showing that the abnormal soft TO phonon in rocksalt-structured ultrawide-bandgap BeO (ref. 5) is mainly induced by a substantial reduction in the short-range bonding interaction due to the Be-O bond stretching caused by an electron cloud-overlap-induced Coulomb repulsion between two adjacent oxygen ions that are arranged octahedrally around an extremely small Be ion. We further demonstrate the emergence of robust ferroelectricity in strain-induced perovskite BaZrO3 and ultrathin HfO2 and ZrO2 films6,7 grown epitaxially on lattice-mismatched SiO2/Si substrate arising from the softening of the TO phonon driven by a reduction in the short-range bonding strength of biaxial strain-induced stretching bonds. These findings shed light on developing a unified theory for ferroelectricity enhancement in ultrathin films free from depolarization fields by tailoring chemical bonds using ionic radius differences, strains, doping and lattice distortions.

Gate-driven transition temperatures of electron hopping behaviors in Hubbard bands formed by dopant-induced QD array in silicon nanowire

Abstract Dopant atoms confined in silicon nanoscale channel can be ionized to form quantum dots (QDs). Several dopant atoms couple with each other forming energy bands, where the electron hopping behavior can be described by the Hubbard model. This characteristic renders dopant-induced quantum dots particularly appealing for applications in nanoelectronic and quantum devices. Herein we study the gate-driven transition temperatures of electron hopping behavior in upper and lower Hubbard bands formed by dopant-induced QD array in junctionless silicon nanowire transistors. The gate-dependent transition temperatures are calculated for three stages of electron hopping behaviors including Efros-Shklovskii Variable Range Hopping (ES-VRH), Mott Variable Range Hopping (Mott-VRH) and Nearest Neighbor Hopping (NNH). Our experimental results indicate that the ES-VRH in arrays of dopant atoms occurs in the domination of a long-range Coulomb interaction, in which the hopping distance relies on the Coulomb gap. Furthermore, the localization length of ES-VRH can be modulated by gate voltages.Those factors lead to the significant difference of transition temperatures between the upper and lower Hubbard bands. In addition, we find that the source-drain bias voltage can effectively modulate the transition temperatures between VRH and NNH by thermal activation energies under different bias voltages Vds.

Spectral functions of lattice fermions on the honeycomb lattice with Hubbard and long-range Coulomb interactions

Spectral functions of lattice fermions on the honeycomb lattice with Hubbard and long-range Coulomb interactions

Molecular dynamics simulation for phase transition of CsPbI3 perovskite with the Buckingham potential.

The CsPbI3 perovskite is a promising candidate for photovoltaic applications, for which several critical phase transitions govern both its efficiency and stability. Large-scale molecular dynamics simulations are valuable in understanding the microscopic mechanisms of these transitions, in which the accuracy of the simulation heavily depends on the empirical potential. This study parameterizes two efficient and stable empirical potentials for the CsPbI3 perovskite. In these two empirical potentials, the short-ranged repulsive interaction is described by the Lennard-Jones model or the Buckingham model, while the long-ranged Coulomb interaction is summed by the damped shifted force method. Our molecular dynamics simulations show that these two empirical potentials accurately capture the γ ↔ β ↔ α and δ → α phase transitions for the CsPbI3 perovskite. Furthermore, they are up to two orders of magnitude more efficient than previous empirical models, owing to the high efficiency of the damped shifted force truncation treatment for the Coulomb interaction.

Direct tracking of H2 roaming reaction in real time

Roaming is an unconventional type of molecular reaction where fragments, instead of immediately dissociating, remain weakly bound due to long-range Coulombic interactions. Due to its prevalence and ability to form new molecular compounds, roaming is fundamental to photochemical reactions in small molecules. However, the neutral character of the roaming fragment and its indeterminate trajectory make it difficult to identify experimentally. Here, we introduce an approach to image roaming, utilizing intense, femtosecond IR radiation combined with Coulomb explosion imaging to directly reconstruct the momentum vector of the neutral roaming H2, a precursor to H3+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{{{{{{\\rm{H}}}}}}}}_{3}}^{+}$$\\end{document} formation, in acetonitrile, CH3CN. This technique provides a kinematically complete picture of the underlying molecular dynamics and yields an unambiguous experimental signature of roaming. We corroborate these findings with quantum chemistry calculations, resolving this unique dissociative process.

KelbgLIP: Program implementation of the high-temperature Kelbg density matrix for path integral and molecular dynamics simulations with long-range Coulomb interaction

In this paper, we present the KelbgLIP code to implement the previously obtained analytical density matrix that includes Coulomb long-range interactions. The method is based on the work of G. Kelbg, who derived a high temperature density matrix for the Coulomb potential. To include all long-range interactions in the density matrix, we use the Ewald technique, specifically the angular-averaged Ewald potential (AAEP). The solution of the Blöch equation within the AAEP has a direct analytic form that can be easily implemented in classical and quantum Monte Carlo or molecular dynamics codes, including exchange effects. The potential part of the density matrix remains finite at small distances, preventing the collapse of a two-component system. Using KelbgLIP, one can calculate the diagonal Kelbg-AAE pseudopotential and the pair density matrix. In the case of a hydrogen plasma, the code is able to calculate action, kinetic and potential energy in the path integral representation. We validated our approach by simulating a nondegenerate weakly coupled hydrogen plasma and obtained the thermodynamic limit in agreement with the Debye-Hückel approximation. In addition, we observe the agreement with classical simulations using the unbounded from below AAEP, which is possible in the weakly-coupled regime. Program summaryProgram Title:KelbgLIP, version 1.0CPC Library link to program files:https://doi.org/10.17632/p773jhdz69.1Licensing provisions: GPLv3Programming language: C++11Nature of problem: The calculation of thermodynamic properties of two-component Coulomb systems relies on the formalism of the density matrix to avoid the collapse due to the unbounded Coulomb potential. The direct consideration of long-range Coulomb potential interactions with periodic boundary conditions requires the solution of the Blöch equation for the density matrix in the case of the Ewald potential. However, typically only the solution for the Coulomb potential is used, omitting all long-range effects, because the Ewald potential has a sufficiently complicated form.Solution method: To account for long-range effects in solving the Blöch equation, one can use the angular-averaged Ewald potential (AAEP). This potential, with its simple analytic form, effectively captures the long-range effects and has a finite interaction range. In order to solve the Blöch equation with the AAEP, we use the Kelbg approach [1], in which the solution was obtained for the Coulomb potential in a high-temperature limit. Hence, we derive the density matrix with the Kelbg-AAE pseudopotential (Kelbg-AAEPP) that is finite at small distances [2]. Notably, this density matrix has a direct analytic form, which avoids a summation over Coulomb energy levels or squaring method [3]. The Kelbg-AAE density matrix is then used in quantum simulations via path integral Monte Carlo and in classical simulations using the diagonal Kelbg-AAEPP with a finite interaction radius. In the case of Boltzmannons, the expressions for action, kinetic and potential energy are derived. Special attention is paid to the calculation involving the non-diagonal Kelbg-AAEPP. The code calculates the diagonal Kelbg-AAEPP with possible improvement at short distances [4], pair Kelbg-AAE density matrix, as well as action, kinetic energy, and potential energy. These routines can be easily integrated into other molecular dynamics or path integral Monte Carlo codes designed for fermions and bosons, which is particularly valuable for the simulations of two-component Coulomb systems.Additional comments including restrictions and unusual features: GSL library version 2.x is required for compilation.

Dimensionality-driven power-law gap in the bilayer TaTe2 grown by molecular-beam epitaxy

Reducing dimensionality can induce profound modifications to the physical properties of a system. In two-dimensional TaS2 and TaSe2, the charge-density wave phase accompanies a Mott transition, thus realizing the strongly correlated insulating state. However, this scenario deviates from TaTe2 due to p–d hybridization, resulting in a substantial contribution of Te 5p at the Fermi level. Here, we show that, differently from the Mott insulating phase of its sister compounds, bilayer TaTe2 hosts a power-law (V-shaped) gap at the Fermi level reminiscent of a Coulomb gap. It suggests the possible role of unscreened long-range Coulomb interactions emerging in lowered dimensions, potentially coupled with a disordered short-range charge-density wave. Our findings reveal the importance of long-range interactions sensitive to interlayer screening, providing another venue for the interplay of complex quantum phenomena in two-dimensional materials.

Strong Raman enhancement in structured colloids: localization of light

Raman spectroscopy is a powerful technique for studying the interaction between light and matter. Here we show a significant enhancement of Raman emission over a broad range of pumping wavelengths from strongly scattering media comprising spatially correlated photonic structures of core–shell TiO2@Silica scatterers mixed with silica nanoparticles and suspended in ethanol. Long-range Coulomb interactions between nanoparticles inside these photonic colloidal structures induce a correlation in the scatterers’ positions (TiO2@Silica), affecting local and global photonic properties. The anomalous enhancement in Raman signal increases as the scattering strength is increased (through either scatterer concentration or pumping wavelength); however, the signal strength continues to behave linearly with excitation power, ruling out classical nonlinear and interferential phenomena. These observations may indicate strong photon correlation in strongly localized electromagnetic modes, inducing successive photon interactions with the atoms or molecules. Aside from the fundamental relevance to understanding measurable properties in this regime of strongly localized electromagnetic modes, our demonstration of strongly enhanced Raman emission over a broad range of pumping wavelengths provides new opportunities for the development of advanced photonic materials and devices.

Calculation of the Matrix Elements of the Long-Range Coulomb Interaction Comparison of the GTO and STO Approaches

Calculation of the Matrix Elements of the Long-Range Coulomb Interaction Comparison of the GTO and STO Approaches

Long-Range Effects in Topologically Defective Arm-Chair Graphene Nanoribbons.

The electronic structure of 7/9-AGNR superlattices with up to eight unit cells has been studied by means of state-of-the-art Density Functional Theory (DFT) and also by two model Hamiltonians, the first one including only local interactions (Hubbard model, Hu) while the second one is extended to allow long-range Coulomb interactions (Pariser, Parr and Pople model, PPP). Both are solved within mean field approximation. At this approximation level, our calculations show that 7/9 interfaces are better described by spin non-polarized solutions than by spin-polarized wavefunctions. Consequently, both Hu and PPP Hamiltonians lead to electronic structures characterized by a gap at the Fermi level that diminishes as the size of the system increases. DFT results show similar trends although a detailed analysis of the density of states around the Fermi level shows quantitative differences with both Hu and PPP models. Before improving model Hamiltonians, we interpret the electronic structure obtained by DFT in terms of bands of topological states: topological states localized at the system edges and extended bulk topological states that interact between them due to the long-range Coulomb terms of Hamiltonian. After careful analysis of the interaction among topological states, we find that the discrepancy between ab initio and model Hamiltonians can be resolved considering a screened long-range interaction that is implemented by adding an exponential cutoff to the interaction term of the PPP model. In this way, an adjusted cutoff distance λ=2 allows a good recovery of DFT results. In view of this, we conclude that the correct description of the density of states around the Fermi level (Dirac point) needs the inclusion of long-range interactions well beyond the Hubbard model but not completely unscreened as is the case for the PPP model.

Electron screening and strength of long-range Coulomb interactions in black phosphorene: From bulk to nanoribbon

Electron screening and strength of long-range Coulomb interactions in black phosphorene: From bulk to nanoribbon

Variational principles for the hydrodynamics of the classical one-component plasma

Hydrodynamic equations for a one-component plasma are derived as a unification of the Euler equations with long-range Coulomb interaction. By using a variational principle, these equations self-consistently unify thermodynamics, dispersion laws, nonlinear motion, and conservation laws. In the moderate and strong coupling limits, it is argued that these equations work down to the length scale of the interparticle spacing. The use of a variational principle also ensures that closure is achieved self-consistently. Hydrodynamic equations are evaluated in both the Eulerian frame, where the fluid variables depend on the position in the laboratory, and the Lagrangian frame, where they depend on the position in some reference state, such as the initial position. Each frame has its advantages and our final theory combines elements of both. The properties of longitudinal and transverse dispersion laws are calculated for the hydrodynamic equations. A simple step function approximation for the pair distribution function enables simple calculations that reveal the structure of the equations of motion. The obtained dispersion laws are compared to molecular dynamics simulations and the theory of quasilocalized charge approximation. The action, which gives excellent agreement for both longitudinal and transverse dispersion laws for a wide range of coupling strengths, is elucidated. Agreement with numerical experiments shows that such a hydrodynamic approach can be used to accurately describe a one-component plasma at very small length scales comparable to the average interparticle spacing. The validity of this approach suggests considering nonlinear flows and other systems with long-range interactions in the future.

Doping-dependent charge- and spin-density wave orderings in a monolayer of Pb adatoms on Si(111)

In this work we computed the phase diagram as a function of temperature and doping for a system of lead adatoms allocated periodically on a silicon (111) surface. This Si(111):Pb material is characterized by a strong and long-ranged Coulomb interaction, a relatively large value of the spin-orbit coupling, and a structural phase transition that occurs at low temperature. In order to describe the collective electronic behavior in the system, we perform many-body calculations consistently taking all these important features into account. We find that charge- and spin-density wave orderings coexist with each other in several regions of the phase diagram. This result is in agreement with the recent experimental observation of a chiral spin texture in the charge density wave phase in this material. We also find that the geometries of the charge and spin textures strongly depend on the doping level. The formation of such a rich phase diagram in the Si(111):Pb material can be explained by a combined effect of the lattice distortion and electronic correlations.

Charged particle scattering in harmonic traps

The trap method provides a novel way to extract phase shifts of neutral-particle scattering from bound-state calculations. It has been adopted successfully in several ab initio calculations to study neutron-nucleus scattering, where there is no long-range Coulomb interaction between the target and projectile. How to incorporate the effects of Coulomb interaction is a crucial problem in the trap method. In this Letter, we examine the robustness of the new proposed Coulomb-corrected Busch-Englert-Rzażewski-Wilkens (BERW) formula Guo (2021) [25] by taking proton-proton scattering as the test ground. While the numerical results are generally well consistent with conventional methods, a number of anomalous scattering energies are identified, where the Coulomb-corrected BERW formula gives less satisfactory results. The underlying theoretical reasons are analyzed in depth, which contributes to a more complete understanding of the applicable scope of the Coulomb-corrected BERW formula. Our study lays the key foundation for future ab initio studies of scattering processes between proton and light nuclei based on the trap method.

Mapping charge excitations in generalized Wigner crystals.

Transition metal dichalcogenide-based moiré superlattices exhibit strong electron-electron correlations, thus giving rise to strongly correlated quantum phenomena such as generalized Wigner crystal states. Evidence of Wigner crystals in transition metal dichalcogenide moire superlattices has been widely reported from various optical spectroscopy and electrical conductivity measurements, while their microscopic nature has been limited to the basic lattice structure. Theoretical studies predict that unusual quasiparticle excitations across the correlated gap between upper and lower Hubbard bands can arise due to long-range Coulomb interactions in generalized Wigner crystal states. However, the microscopic proof of such quasiparticle excitations is challenging because of the low excitation energy of the Wigner crystal. Here we describe a scanning single-electron charging spectroscopy technique with nanometre spatial resolution and single-electron charge resolution that enables us to directly image electron and hole wavefunctions and to determine the thermodynamic gap of generalized Wigner crystal states in twisted WS2 moiré heterostructures. High-resolution scanning single-electron charging spectroscopy combines scanning tunnelling microscopy with a monolayer graphene sensing layer, thus enabling the generation of individual electron and hole quasiparticles in generalized Wigner crystals. We show that electron and hole quasiparticles have complementary wavefunction distributions and that thermodynamic gaps of ∼50 meV exist for the 1/3 and 2/3 generalized Wigner crystal states in twisted WS2.

Reactive force field potential with shielded long-range Coulomb interaction: Application to graphene–water capacitors

Electrode–electrolyte interfacial properties characterize the functioning of electrochemical devices, and reactive molecular dynamics simulations, using reactive force fields (ReaxFF) and charge equilibration (QEq) techniques, are classical atomistic methods for investigating the processes that govern the device properties. However, the numerical implementation of ReaxFF and QEq treats Coulomb interaction with a short-distance cutoff for computational speed, thereby limiting interactions among atoms to a domain containing only their neighbor lists. Excluding long-distance Coulomb interactions makes the description of electrostatics in large-scale systems intractable. We apply Ewald sum in the extension of ReaxFF to include long-range Coulomb (LRC) interactions and investigate the effect of the inclusion on the electrostatic and capacitive properties of graphene–water interfaces at different applied potentials in comparison with the original ReaxFF. The study shows that with the inclusion of long-range Coulomb, the capacitance amounts to 4.9 ± 0.2 μF cm−2 compared with 4.4 ± 0.2 μF cm−2 predicted by the original ReaxFF [with short-range Coulomb (SRC)]; thus, indicating that SRC underestimates the capacitance of water between graphene walls by 12% when compared with the 5.0 μF cm−2 predicted with the extended simple point charge (SPC/E) water model. Thus, the results indicate that LRC ReaxFF/QEq have the ability and advantage to model electrochemical processes at a more realistic Coulomb interaction description and foster the processing of the details about the operation of electrochemical devices than the SRC.

Ionic coulomb drag in nanofluidic semiconductor channels for energy harvest

The onset of electronic current in a doped silicon membrane induced by the long-range Coulomb interaction of ions flowing through a nanofluidic channel is established by a combined computational and analytical approach based on Green’s function technique and Boltzmann transport formalism. Characterized by an open circuit voltage and short circuit current, the electronic Coulomb drag provides a new paradigm for power harvesting. In addition, our model predicts a current amplification of the ionic drag current because of the large momentum transfer from heavy ions to charge carriers in silicon, which is achieved for both anions and cations flowing in the nanochannel irrespective of the dopant type in the semiconductor. The analysis indicates the versatility of this effect with respect to the nature of the electrolyte and the semiconducting materials, providing proper tuning of their structures and design configurations.

The empirical coupled-channel model with the new analytical penetration formula for fusion cross-sections

The new analytical barrier penetration formula proposed by Li et al. [Int. J. Mod. Phys. E 19 (2010) 359] for potential barriers containing a long-range Coulomb interaction is adopted in the empirical coupled-channel (ECC) model for calculating fusion cross-sections. As compared with the Hill–Wheeler (HW) formula based on the parabolic approximation, this formula is more appropriate for the barrier penetration with incident energies much lower than the Coulomb barrier. The calculated results show that the ECC model with the new barrier penetration formula can describe the fusion cross-section data well, especially for light systems at energies much lower than the Coulomb barrier. Then the systematics of the difference between the ECC calculation with the new penetration formula and that with the HW formula is investigated. The results show that the difference between the results with the HW formula and the new penetration formula is less than one order of magnitude at [Formula: see text].