Long-range Coulomb Interaction Research Articles

Development of a new quantum trajectory molecular dynamics framework.

An extension to the wave packet description of quantum plasmas is presented, where the wave packet can be elongated in arbitrary directions. A generalized Ewald summation is constructed for the wave packet models accounting for long-range Coulomb interactions and fermionic effects are approximated by purpose-built Pauli potentials, self-consistent with the wave packets used. We demonstrate its numerical implementation with good parallel support and close to linear scaling in particle number, used for comparisons with the more common wave packet employing isotropic states. Ground state and thermal properties are compared between the models with differences occurring primarily in the electronic subsystem. Especially, the electrical conductivity of dense hydrogen is investigated where a 15% increase in DC conductivity can be seen in our wave packet model compared with other models. This article is part of the theme issue 'Dynamic and transient processes in warm dense matter'.

Structural Evolution of Cadmium Selenide Clusters: An Unbiased Global Optimization Study of (CdSe)N for 5 ≤ N ≤ 80.

The structures of large cadmium selenide clusters are poorly understood due to the presence of challenging long-range Coulombic interactions and a vast number of possible structures. In this study, we present an unbiased fuzzy global optimization method that incorporates atom-pair hopping, ultrafast shape recognition, and adaptive temperatures within a directed Monte Carlo framework to enhance the search efficiency of binary clusters. Using this method and first-principles calculations, we successfully obtain the lowest-energy structures of (CdSe)N clusters with 5 ≤ N ≤ 80. The putative global minima reported in the literature have been obtained. The binding energy per atom tends to decrease with cluster size. Our results show that the stable structures evolve from rings to stacked rings, cages, nanotubes, cage-wurtzite, cage-core, and finally wurtzite structures, enabling us to reveal a systematic structural evolution for the growth of cadmium selenide clusters without ligands.

Magnetism and quantum melting in moiré-material Wigner crystals

Semiconductor moir\'e materials host generalized Wigner crystal states at a series of fractional fillings, originating from localization of electrons in a subset of moir\'e sites in order to minimize long-range Coulomb interactions. Using exact diagonalization calculations, this paper studies the interplay between spin and charge degrees of freedom that gives rise to different magnetic orders within the crystalline states at fillings $\ensuremath{\nu}$=1/3 and $\ensuremath{\nu}$=2/3. The authors provide effective spin model descriptions of those phases, also addressing their Mott-Wigner melting transitions.

Superconductivity in Ce-based cage compounds

Cerium-based ternary compounds CeNi2Cd20 and CePd2Cd20 do not exhibit long-range order down to millikelvin temperature range. Given the large separation between Ce ions which significantly reduces the super-exchange interactions and vanishingly small Ruderman–Kittel–Kasuya–Yosida interaction, here we show that nodal superconductivity mediated by the valence fluctuations must be a ground state in these materials. We propose that the critical temperature for the superconducting transition can be significantly increased by applying hydrostatic pressure. We employ an extended periodic Anderson lattice model which includes the long-range Coulomb interactions between the itinerant electrons as well as the local Coulomb interaction between the predominantly localized and itinerant electrons to compute a critical temperature of the superconducting transition. Using the slave-boson approach we show that fluctuations mediated by the repulsive electron–electron interactions lead to the emergence of d-wave superconductivity.

Hole density dependent magnetic structure and anisotropy in Fe-pnictide superconductor

The competition between different magnetic structures in hole-doped Fe-pnicitides is explored based on an extended five-orbital Hubbard model including long-range Coulomb interactions. Our results show that the stabilized magnetic structure evolves with increasing hole doping level. Namely, the stripe antiferromagnetic phase dominates at zero doping, while magnetic structures with more antiferromagnetic linking numbers such as the staggered tetramer, staggered trimer, and staggered dimer phases become energetically favorable as the hole density increases. At a certain doping level, energy degeneracy of different magnetic structures appears, indicating strong magnetic frustration and magnetic fluctuations in the system. We suggest that the magnetic competition induced by the hole doping may explain the fast decrease of the Neel temperature T N and the moderately suppressed magnetic moment in the hole doped Fe-pnicitides. Moreover, our results show a sign reversal of the kinetic energy anisotropy as the magnetic ground state evolves, which may be the mechanism behind the puzzling sign reversal of the in-plane resistivity anisotropy in hole-doped Fe-pnicitides.

Following the Higgs mode across the BCS-BEC crossover in two dimensions

Although substantial effort has been dedicated to analyzing the Higgs (amplitude) mode in superconducting systems, there are relatively few studies of the Higgs peak's dispersion and width, quantities which are observable in spectroscopic measurements. These properties can be obtained from the location of the pole of the amplitude (Higgs) susceptibility in the lower half plane of complex frequency. We analyze the behavior of the Higgs mode in a two-dimensional neutral fermionic superfluid at $T=0$ throughout the crossover from Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) behavior. This occurs when the dressed chemical potential $\ensuremath{\mu}$ changes sign from positive to negative. For $\ensuremath{\mu}>0$, we find a pole in the Higgs susceptibility in the lower half plane of frequency and demonstrate that it leads to a well-defined peak in spectroscopic probes. For $\ensuremath{\mu}<0$, the pole still exists but is ``hidden,'' not giving rise to a peak in spectroscopic probes. Extending this analysis to a charged superconductor, we find that the Higgs mode is unaffected by the long-range Coulomb interaction.

Ordered photonic colloidal suspensions.

Ordered photonic structures (photonic crystals) have seen increasing interest in recent years due to their potential applications, which depend on fabrication technologies suitable for mass production. In this paper, we studied by light diffraction the order in photonic colloidal suspensions composed by core-shell (T i O 2@S i l i c a) nanoparticles suspended in ethanol and water solutions. Light diffraction measurements show order in these photonic colloidal suspensions, being stronger in ethanol compared with suspensions in water. Strong and long-range Coulomb interaction explains the order and correlation in the scatterers' (T i O 2@S i l i c a) position, which favors significantly the interferential processes as localization of light.

Numerical investigation of electrostatic force density in ionic crystals such as NaCl

We investigate the density of electrostatic force in a continuous medium modeled as an ionic crystal similar to that of NaCl. The theoretical model is three-dimensional and consists of a lattice of ions of alternating signs. The ions can interact with each other and the externally applied electric field and pressure via elastic springs, which model short-range chemical bonds, and long-range Coulomb interactions. The condition of equilibrium can be solved numerically to yield the basic physical parameters of the structure including Young's modulus, the dielectric permittivity, and the electrically induced strain. We then compare these results to the theoretical predictions obtained according to various formulas for the electrostatic force density that can be found in the literature. It is shown that Helmholtz force density predicts the numerically computed strain almost perfectly while other expressions result in large errors. The numerical simulations are limited to statics.

Collective density fluctuations of strange metals with critical Fermi surfaces

Recent spectroscopic measurements in a number of strongly correlated metals that exhibit non-Fermi liquid like properties have observed evidence of anomalous frequency and momentum-dependent charge-density fluctuations. Specifically, in the strange metallic regime of the cuprate superconductors, there is a featureless particle-hole continuum exhibiting unusual power-laws, and experiments suggest that the plasmon mode decays into this continuum in a manner that is distinct from the expectations of conventional Fermi liquid theory. Inspired by these new experimental developments, we address the nature of low-energy collective modes and the particle-hole continua for different "solvable" lattice models of non-Fermi liquids that host a critical Fermi surface -- a sharp electronic Fermi surface without any low-energy electronic quasiparticles. We scrutinize theoretically the possible existence of a long-lived zero-sound mode, which is renormalized to the plasma frequency in the presence of long-ranged coulomb interactions, and its decay into the continuum over a wide range of frequencies and momenta. Quite remarkably, some of the models analyzed here can account for certain aspects of the universal experimental observations, that clearly lie beyond the purview of standard Fermi liquid theory.

Valley-Tunable Even-Denominator Fractional Quantum Hall State in the Lowest Landau Level of an Anisotropic System.

Fractional quantum Hall states (FQHSs) at even-denominator Landau level filling factors (ν) are of prime interest as they are predicted to host exotic, topological states of matter. We report here the observation of a FQHS at ν=1/2 in a two-dimensional electron system of exceptionally high quality, confined to a wide AlAs quantum well, where the electrons can occupy multiple conduction-band valleys with an anisotropic effective mass. The anisotropy and multivalley degree of freedom offer an unprecedented tunability of the ν=1/2 FQHS as we can control both the valley occupancy via the application of in-plane strain, and the ratio between the strengths of the short- and long-range Coulomb interaction by tilting the sample in the magnetic field to change the electron charge distribution. Thanks to this tunability, we observe phase transitions from a compressible Fermi liquid to an incompressible FQHS and then to an insulating phase as a function of tilt angle. We find that this evolution and the energy gap of the ν=1/2 FQHS depend strongly on valley occupancy.

Observation of a massive phason in a charge-density-wave insulator.

The lowest-lying fundamental excitation of an incommensurate charge-density-wave material is believed to be a massless phason-a collective modulation of the phase of the charge-density-wave order parameter. However, long-range Coulomb interactions should push the phason energy up to the plasma energy of the charge-density-wave condensate, resulting in a massive phason and fully gapped spectrum1. Using time-domain terahertz emission spectroscopy, we investigate this issue in (TaSe4)2I, a quasi-one-dimensional charge-density-wave insulator. On transient photoexcitation at low temperatures, we find the material strikingly emits coherent, narrowband terahertz radiation. The frequency, polarization and temperature dependences of the emitted radiation imply the existence of a phason that acquires mass by coupling to long-range Coulomb interactions. Our observations underscore the role of long-range interactions in determining the nature of collective excitations in materials with modulated charge or spin order.

Enhanced spin-orbit coupling and orbital moment in ferromagnets by electron correlations

In atomic physics, the Hund's rule states that the largest spin and orbital state is realized due to the interplay of spin-orbit coupling (SOC) and Coulomb interactions. Here, we show that in ferromagnetic solids the effective SOC and the orbital magnetic moment can be dramatically enhanced by a factor of $1/[1\ensuremath{-}(2{U}^{\ensuremath{'}}\ensuremath{-}U\ensuremath{-}{J}_{H}){\ensuremath{\rho}}_{0}]$, where $U$ and ${U}^{\ensuremath{'}}$ are the on-site Coulomb interaction within the same orbitals and between different orbitals, respectively, ${J}_{H}$ is the Hund's coupling, and ${\ensuremath{\rho}}_{0}$ is the average density of states. This factor is obtained by using the two-orbital as well as five-orbital Hubbard models with SOC. We also find that the spin polarization is more favorable than the orbital polarization, being consistent with experimental observations. The theory is also extended to study the spin fluctuations and long-range Coulomb interactions, and can be applied to understand the enhanced orbital magnetic moment and giant Faraday effect in ferromagnetic nanogranules in recent experiments. This present paper provides a fundamental basis for understanding the enhancements of SOC and orbital moment by Coulomb interactions in ferromagnets, which would have wide applications in spintronics.

Efficient calculation of k -integrated electron energy loss spectra: Application to monolayers of MoS2, hBN, and graphene

The theoretical scattering cross section of electron energy loss spectroscopy (EELS) is essentially given by $\ensuremath{-}\text{Im}\phantom{\rule{0.16em}{0ex}}{\ensuremath{\varepsilon}}^{\ensuremath{-}1}(\mathbf{k},\ensuremath{\omega})$ with the energy loss $\ensuremath{\hbar}\ensuremath{\omega}$ and the momentum transfer $\ensuremath{\hbar}\mathbf{k}$. The macroscopic dielectric function $\ensuremath{\varepsilon}(\mathbf{k},\ensuremath{\omega})$ can be calculated from first principles using time-dependent density-functional theory. However, experimental EELS measurements have a finite $\mathbf{k}$ resolution or, when operated in spatial resolution mode, yield a $\mathbf{k}$-integrated loss spectrum, which deviates significantly from EEL spectra calculated for specific $\mathbf{k}$ momenta. On the other hand, integrating the theoretical spectra over $\mathbf{k}$ is complicated by the fact that the integrand varies over several (typically six) orders of magnitude around $k=0$. In this article, we present a stable technique for integrating EEL spectra over an adjustable range of momentum transfers. The important region around $k=0$, where the integrand is nearly divergent, is treated partially analytically, allowing an analytic integration of the near divergence. The scheme is applied to three prototypical two-dimensional systems: monolayers of ${\mathrm{MoS}}_{2}$ (semiconductor), hexagonal BN (insulator), and graphene (semimetal). Here, we are confronted with the added difficulty that the long-range Coulomb interaction leads to a very slow supercell (vacuum size) convergence. We address this difficulty by employing an extrapolation scheme, enabling an efficient reduction of the supercell size and thus a considerable speedup in computation time. The calculated $\mathbf{k}$-integrated spectra are in very favorable agreement with experimental EEL spectra.

An exact formula for the variance of linear statistics in the one-dimensional jellium model

We consider the jellium model of N particles on a line confined in an external harmonic potential and with a pairwise one-dimensional Coulomb repulsion of strength α > 0. Using a Coulomb gas method, we study the statistics of where f(x), in principle, is an arbitrary smooth function. While the mean of s is easy to compute, the variance is nontrivial due to the long-range Coulomb interactions. In this paper we demonstrate that the fluctuations around this mean are Gaussian with a variance for large N. In this paper, we provide an exact compact formula for the constant . In addition, we also calculate the full large deviation function characterizing the tails of the full distribution for several different examples of f(x). Our analytical predictions are confirmed by numerical simulations.

Evidence of the Coulomb gap in the density of states of MoS2

${\mathrm{MoS}}_{2}$ is an emergent van der Waals material that shows promising prospects in semiconductor industry and optoelectronic applications. However, its electronic properties are not yet fully understood. In particular, the nature of the insulating state at low carrier density deserves further investigation, as it is important for fundamental research and applications. In this study we investigate the insulating state of a dual-gated exfoliated bilayer ${\mathrm{MoS}}_{2}$ field-effect transistor by performing magnetotransport experiments. We observe a positive and nonsaturating magnetoresistance, in a regime where only one band contributes to electron transport. At low electron density ($\ensuremath{\sim}1.4\ifmmode\times\else\texttimes\fi{}{10}^{12}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$) and a perpendicular magnetic field of 7 Tesla the resistance exceeds by more than one order of magnitude the zero field resistance and exponentially drops with increasing temperature. We attribute this observation to strong electron localization. Both temperature and magnetic field dependence can, at least qualitatively, be described by the Efros-Shklovskii law, predicting the formation of a Coulomb gap in the density of states due to Coulomb interactions. However, the localization length obtained from fitting the temperature dependence exceeds by more than one order of magnitude the one obtained from the magnetic field dependence. We attribute this discrepancy to the presence of a nearby metallic gate, which provides electrostatic screening and thus reduces long-range Coulomb interactions. The result of our study suggests that the insulating state of ${\mathrm{MoS}}_{2}$ originates from a combination of disorder-driven electron localization and Coulomb interactions.

The intrinsic electrostatic dielectric behaviour of graphite anodes in Li-ion batteries—Across the entire functional range of charge

Lithium–graphite intercalation compounds (Li-GICs) are by far the most common anode material for modern Li-ion batteries. However, the dielectric response of this material in the electrostatic limit and its variation depending on the state of charge (SOC) has not been investigated to a satisfactory degree – neither by means of theory nor by experiment – and especially not for the higher range of SOC. In this work, we – for the first time – predict a mostly linear dependency of the relative permittivity ϵr on the SOC, from ≈7 at SOC 0% to ≈25 at SOC 100%. This is achieved by making use of our recently published DFTB parametrization for Li-GICs based on a machine-learned repulsive potential in order to overcome the computational hurdles of sampling the long-ranged Coulomb interactions within this material. In doing so, we provide novel insight into a property which is highly desired, particularly as an input parameter for charged kinetic Monte Carlo simulations.

Studies of Transient Photoplasma Evolution in an Electrostatic Field: Single Particle Motion to Its Collective Behavior

Though the plasma is an ensemble of charged particles, its behavior in an electrostatic field is different from that of individual particles. It shows a collective behavior as a result of long-range Coulomb interactions among the charged particles. To elucidate the plasma behavior, the transient evolution of photoplasma in an applied electrostatic field is carried out in two different density regimes where the plasma shows its single particle motion and collective behavior. In the case of low-density plasma, the external electric field dominates the plasma motion. The electrons and ions act as two independent entities and the plasma shows its single particle behavior in the external field, whereas in the high-density plasma regime, the self-generated electric field in the plasma is comparable to the applied external field. The plasma motion is governed by both the internal ambipolar electric field in the plasma as well as the applied electrostatic field. Thus, the plasma shows its collective motion due to Coulomb interactions among the charged particles.

Coulomb Force from Non-Local Self-Assembly of Multi-Peak Densities in a Charged Space Continuum

Maxwell’s electrodynamics admits radial charge densities of the elementary organization with one vertex of the spherical symmetry. A multi-vertex distribution of sharply inhomogeneous charge densities can also be described by monistic field solutions to Maxwell’s equations–equalities. Coulomb–Lorentz forces are exerted locally to correlated electric densities in their volume organization with the fixed self-energy integral. The long-range Coulomb interaction between the dense peaks of the charged space continuum can be described quantitatively through bulk integrals of local tensions within observable bodies in favor of the monistic all-unity in the material space physics of Descartes and Russian cosmists.

Evidence of frustrated magnetic interactions in a Wigner-Mott insulator.

Electrons in two-dimensional semiconductor moiré materials are more delocalized around the lattice sites than those in conventional solids1,2. The non-local contributions to the magnetic interactions can therefore be as important as the Anderson superexchange3, which makes the materials a unique platform to study the effects of competing magnetic interactions3,4. Here we report evidence of strongly frustrated magnetic interactions in a Wigner-Mott insulator at a two-thirds (2/3) filling of the moiré lattice in angle-aligned WSe2/WS2 bilayers. Magneto-optical measurements show that the net exchange interaction is antiferromagnetic for filling factors below 1 with a strong suppression at a 2/3 filling. The suppression is lifted on screening of the long-range Coulomb interactions and melting of the Wigner-Mott insulators by a nearby metallic gate. The results can be qualitatively captured by a honeycomb-lattice spin model with an antiferromagnetic nearest-neighbour coupling and a ferromagnetic second-neighbour coupling. Our study establishes semiconductor moiré materials as a model system for lattice-spin physics and frustrated magnetism5.

Thermodynamic Characteristic for a Correlated Flat-Band System with a Quantum Anomalous Hall Ground State.

While the ground-state phase diagram of the correlated flat-band systems has been intensively investigated, the dynamic and thermodynamic properties of such lattice models are less explored, but it is the latter which is most relevant to the experimental probes (transport, quantum capacitance, and spectroscopy) of the quantum moiré materials such as twisted bilayer graphene. Here we show, by means of momentum-space quantum MonteCarlo and exact diagonalization, in chiral limit there exists a unique thermodynamic characteristic for the correlated flat-band model with interaction-driven quantum anomalous Hall (QAH) ground state, namely, the transition from the QAH insulator to the metallic state takes place at a much lower temperature compared with the zero-temperature single-particle gap generated by the long-range Coulomb interaction. Such low transition temperature comes from the proliferation of excitonic particle-hole excitations, which transfers the electrons across the gap between different topological bands to restore the broken time-reversal symmetry and gives rise to a pronounced enhancement in the charge compressibility. Future experiments, to verify such generic thermodynamic characteristics, are proposed.