Bare Coulomb Research Articles

Going Beyond the GW Approximation Using the Time-Dependent Hartree-Fock Vertex.

The time-dependent Hartree-Fock (TDHF) vertex of many-body perturbation theory (MBPT) makes it possible to extend TDHF theory to charged excitations. Here we assess its performance by applying it to spherical atoms in their neutral electronic configuration. On a theoretical level, we recast the TDHF vertex as a reducible vertex, highlighting the emergence of a self-energy expansion purely in orders of the bare Coulomb interaction; then, on a numerical level, we present results for polarizabilities, ionization energies (IEs), and photoemission satellites. We confirm the superiority of THDF over simpler methods such as the random phase approximation for the prediction of atomic polarizabilities. We then find that the TDHF vertex reliably provides better IEs than GW and low-order self-energies do in the light-atom, few-electron regime; its performance degrades in heavier, many-electron atoms instead, where an expansion in orders of an unscreened Coulomb interaction becomes less justified. New relevant features are introduced in the satellite spectrum by the TDHF vertex, but the experimental spectra are not fully reproduced due to a missing account of nonlinear effects connected to hole relaxation. We also explore various truncations of the self-energy given by the TDHF vertex, but do not find them to be more convenient than low-order approximations such as GW and second Born (2B), suggesting that vertex corrections should be carried out consistently both in the self-energy and in the polarizability.

Basis-Set-Error-Free Random-Phase Approximation Correlation Energies for Atoms Based on the Sternheimer Equation.

The finite basis set errors for all-electron random-phase approximation (RPA) correlation energy calculations are analyzed for isolated atomic systems. We show that, within the resolution-of-identity (RI) RPA framework, the major source of the basis set errors is the incompleteness of the single-particle atomic orbitals used to expand the Kohn-Sham eigenstates, instead of the auxiliary basis set (ABS) to represent the density response function χ0 and the bare Coulomb operator v. By solving the Sternheimer equation for the first-order wave function on a dense radial grid, we are able to eliminate the major error─the incompleteness error of the single-particle atomic basis set─for atomic RPA calculations. The error stemming from a finite ABS can be readily rendered vanishingly small by increasing the size of the ABS, or by iteratively determining the eigenmodes of the χ0v operator. The variational property of the RI-RPA correlation energy can be further exploited to optimize the ABS in order to achieve fast convergence of the RI-RPA correlation energy. These numerical techniques enable us to obtain basis-set-error-free RPA correlation energies for atoms, and in this work, such energies for atoms from H to Kr are presented. The implications of the numerical techniques developed in the present work for addressing the basis set issue for molecules and solids are discussed.

Many-body theory calculations of positron scattering and annihilation in noble-gas atoms via the solution of Bethe–Salpeter equations using the Gaussian-basis code EXCITON+

Scattering phase shifts and annihilation rates for low-energy positrons interacting with noble gas atoms are calculated ab initio using many-body theory implemented in the Gaussian-orbital code EXCITON+. Specifically, we construct the positron–atom correlation potential (self-energy) as the sum of three classes of infinite series describing the screened polarization, virtual positronium formation, and positron-hole repulsion found via the solution of Bethe–Salpeter equations for the two-particle propagators. The normalization of the continuum states is determined using the shifted pseudostates method [A. R. Swann and G. F. Gribakin, Phys. Rev. A 101, 022702 (2020)]. Comparison with the previous sophisticated B-spline many-body approach, which is restricted to atoms [J. Ludlow, D. G. Green, and G. F. Gribakin, Phys. Rev. A 90, 032712 (2014)], validates the EXCITON+ code, which can be used for multicentered targets including molecules, clusters, and condensed matter. Moreover, the relative effects of higher-order diagrams are quantified. It is found that the screening of the electron–positron Coulomb interaction represented by the infinite ring-diagram series (random-phase approximation) is compensated effectively by the additional electron-hole attraction corrections to it (the Bethe–Salpeter equation approximation) and that the use of the screened Coulomb interaction (screened at BSE level) in place of the bare Coulomb interaction in the virtual positronium and positron-hole ladder diagrams has negligible effect on both the phase shifts and Zeff. Our scattering length for Ne and Kr is in improved agreement with the convergent close-coupling result, and for Ar, the scattering length is in better agreement with the experiment compared with the previous B-spline many-body approach.

Exciton dissociation mediated by phonons in organic photovoltaics

It is well known that phonons can overscreen the bare Coulomb electron-electron repulsion, turning it into the effective attraction that binds the Cooper pairs responsible for BCS superconductivity. Here, we use a simple lattice model to prove that the counterpart of this is also possible, whereby phonons overscreen the bare electron-hole attraction and may turn it repulsive at short distances, driving exciton dissociation in certain regions of the parameter space. We argue that this phonon-mediated short-range screening may play an important role in the physics of organic solar cell materials (and other materials with strong electron-phonon coupling) and could point the way to new strategies for optimizing their efficiencies.

Like‐charge attraction in one‐and two‐dimensional Coulomb systems

AbstractThe bare Coulomb interaction between two like‐charges is repulsive. When these charges are immersed in an electrolyte, the thermal fluctuations of the ions turn the bare Coulomb interaction into an effective interaction between the two charges. An interesting question arises: is it possible that the effective interaction becomes attractive for like‐charges? We will show how this like‐charge attraction phenomenon is indeed predicted in some one‐and two‐dimensional models of Coulomb systems. Exact analytical results can be obtained for these Coulomb systems models due to some connections that they have with integrable field theories. We will explain the techniques that allow obtaining exact results for the correlation functions between like‐charge particles and how, under certain circumstances, the natural repulsion interaction shifts to being attractive. Although the technical details differ for 1d or 2d systems, the physical cause of this phenomenon is rooted in a three‐body interaction between the two like‐charges and an ion of the electrolyte with an opposite charge.

Mediated Interaction between Ions in Quantum Degenerate Gases.

We explore the interaction between two trapped ions mediated by a surrounding quantum degenerate Bose or Fermi gas. Using perturbation theory valid for weak atom-ion interaction, we show analytically that the interaction mediated by a Bose gas has a power-law behavior for large distances whereas it has a Yukawa form for intermediate distances. For a Fermi gas, the mediated interaction is given by a power law for large density and by a Ruderman-Kittel-Kasuya-Yosida form for low density. For strong atom-ion interaction, we use a diagrammatic theory to demonstrate that the mediated interaction can be a significant addition to the bare Coulomb interaction between the ions, when an atom-ion bound state is close to threshold. Finally, we show that the induced interaction leads to substantial and observable shifts in the ion phonon frequencies.

Stochastic many-body calculations of moir\xe9 states in twisted bilayer graphene at high pressures

We introduce three developments within the stochastic many-body perturbation theory: efficient evaluation of off-diagonal self-energy terms, construction of Dyson orbitals, and stochastic constrained random phase approximation. The stochastic approaches readily handle systems with thousands of atoms. We use them to explore the electronic states of twisted bilayer graphene (tBLG) characterized by giant unit cells and correlated electronic states. We document the formation of electron localization under compression; weakly correlated states are merely shifted in energy. We demonstrate how to efficiently downfold the correlated subspace on a model Hamiltonian with a screened frequency-dependent two-body interaction. For the 6° tBLG system, the onsite interactions are between 200 and 300 meV under compression. The Dyson orbitals exhibit spatial distribution similar to the mean-field single-particle states. Under pressure, the electron-electron interactions increase in the localized states; however, the dynamical screening does not fully balance the dominant bare Coulomb interaction.

Wigner Crystallization of Electrons in a One-Dimensional Lattice: A Condensation in the Space of States.

We study the ground state of a system of spinless electrons interacting through a screened Coulomb potential in a lattice ring. By using analytical arguments, we show that, when the effective interaction compares with the kinetic energy, the system forms a Wigner crystal undergoing a first-order quantum phase transition. This transition is a condensation in the space of the states and belongs to the class of quantum phase transitions discussed in [M. Ostilli and C. Presilla, J. Phys. A 54, 055005 (2021).JPAMB51751-811310.1088/1751-8121/aba144]. The transition takes place at a critical value r_{s}_{c} of the usual dimensionless parameter r_{s} (radius of the volume available to each electron divided by effective Bohr radius) for which we are able to provide rigorous lower and upper bounds. For large screening length these bounds can be expressed in a closed analytical form. Demanding MonteCarlo simulations allow to estimate r_{s}_{c}≃2.3±0.2 at lattice filling 3/10 and screening length 10 lattice constants. This value is well within the rigorous bounds 0.7≤r_{s}_{c}≤4.3. Finally, we show that if screening is removed after the thermodynamic limit has been taken, r_{s}_{c} tends to zero. In contrast, in a bare unscreened Coulomb potential, Wigner crystallization always takes place as a smooth crossover, not as a quantum phase transition.

Exact Analytical Solution of the Ground-State Hydrogenic Problem with Soft Coulomb Potential.

We provide the exact analytical solution of the ground-state hydrogenic problem with soft Coulomb potential in 1-, 2- and 3-D. We show that the wave function is an analytical function of the inverse of the soft Coulomb potential and identify a power term, an exponentially decaying term and a mildly varying modulator function on the exponential. In approaching the bare Coulomb limit, only the exponentially decaying term survives in 2D and 3D and converges to the well-known result. This is in contrast with the 1D case, where the wave function shrinks to a delta function with a total energy of minus infinity. The asymptotic behavior of the energy in such limit has been analyzed. Moreover, by analyzing the solution in different dimensions, we find that the total energy increases with dimension and scales linearly rather than quadratically with the nuclear charge Z in the large Z limit.

Strengthening the case for interatomic Coulomb decay as a subdominant reaction channel in slow O3+−Ne2 collisions with independent-atom-model coupled-channel calculations

We report on electron removal calculations for 2.81 keV/amu Li$^{3+}$ and O$^{3+}$ ion collisions with neon dimers. The target is described as two independent neon atoms fixed at the dimer's equilibrium bond length, whose electrons are subjected to the time-dependent bare and screened Coulomb potentials of the classically moving Li$^{3+}$ and O$^{3+}$ projectile ions, respectively. Three mutually perpendicular orientations of the dimer with respect to the rectilinear projectile trajectories are considered and collision events for the two ion-atom subsystems are combined in an impact parameter by impact parameter fashion and are orientation-averaged to calculate probabilities and cross sections for the ion-dimer system. The coupled-channel two-center basis generator method is used to solve the ion-atom collision problems. We concentrate the ion-dimer analysis on one-electron and two-electron removal processes which can be associated with interatomic Coulomb decay, Coulomb explosion, and radiative charge transfer. We find that the calculated relative yields are in fair agreement with recent experimental data for O$^{3+}$-Ne$_2$ collisions if we represent the projectile by a screened Coulomb potential, but disagree markedly for a bare Coulomb potential, i.e., for Li$^{3+}$ impact. In particular, our calculations suggest that interatomic Coulomb decay is a significant reaction channel in the former case only, since capture of a Ne($2s$) electron to form hydrogenlike Li$^{2+}$ is unlikely.

Gate-Induced Metal-Insulator Transition in 2D van der Waals Layers of Copper Indium Selenide Based Field-Effect Transistors.

The existence of an exquisite phenomenon such as a metal-insulator transition (MIT) in two-dimensional (2D) systems, where completely different electronic functionalities in the same system can emerge simply by regulating parameters such as charge carrier density in them, is noteworthy. Such tunability in material properties can lead to several applications where precise tuning of function specific properties are desirable. Here, we report on our observation on the occurrence of MIT in the 2D material system of copper indium selenide (CuIn7Se11). Clear evidence of the metallic nature of conductivity (σ) under the influence of electrostatic doping via the gate, which crosses over to an insulating phase upon lowering the temperature, was observed by investigating the temperature and gate dependence of σ in CuIn7Se11 field-effect transistor devices. At higher charge carrier densities (n > 1012 cm-1), we found that σ ∼ (n)α with α ∼ 2, which suggests the presence of bare Coulomb impurity scattering within the studied range of temperature (280 K > T > 20 K). Our analysis of the conductivity data following the principles of percolation theory of transition where σ ∼ (n - nC)δ show that the critical percolation exponent δ(T) has average values ∼1.57 ± 0.27 and 1.02 ± 0.35 within the measured temperature range for the two devices and it is close to the 2D percolation exponent value of 1.33. We believe that the 2D MIT seen in our system is due to the charge density inhomogeneity caused by electrostatic doping and unscreened charge impurity scattering that leads to a percolation driven transition. The findings reported here for CuIn7Se11 system provide a different material platform to investigate MIT in 2D and are crucial in order to understand the fundamental basis of electronic interactions and charge-transport phenomenon in other unexplored 2D electron systems.

Critical stability and quantum phase transition of screened two‐electron system

AbstractThe ground state energy and structural properties of a model two‐electron system (Zee), bound via screened Coulomb interaction with nuclear charge Z, have been studied under the variational framework. Hylleraas type basis has been adopted for explicit incorporation of the electron–electron correlation. Critical nuclear charges (Zc) of Zee system have been reported for different screening parameters (μ). Expectation values of different structural properties have been estimated to predict the internal structure of the Zee system. The variation of the structural properties with respect to Z for different μ reveals the signature of quantum phase transition (QPT) in the vicinity of Zc. Moreover, the nature of variation of these properties with respect to Z in case of bare Coulomb or free system (μ = 0) is completely opposite to those of screened system (μ ≠ 0). Radial two‐particle density (TPD) confirms the symmetry breaking of the electronic structure and therefore QPT in the vicinity of Zc.

Critical Stability of the Negatively Charged Positronium-Like Ions with Yukawa Potentials and Varying Z

The question of stability of a given quantum system made up of charged particles is of fundamental interest in atomic, molecular, and nuclear physics. In this work, the stability for the negatively charged positronium (Ps)-like ions or the three-body system ( Z e + , e − , e − ) with Yukawa potentials is studied using correlated exponential wavefunctions based on the Ritz variational method. We obtained the critical screening parameter μ C as a function of the continuously varied nuclear charge Z , the critical nuclear charge Z C as a function of the screening parameter μ , and the ionization energies in terms of the screening parameter μ and Z . The critical nuclear charge for the bare Coulomb system ( Z e + , e − , e − ) obtained using 700-term correlated exponential wavefunctions is in accord with the reported results. The ionization energy, μ C , and Z C for the Yukawa system ( Z e + , e − , e − ) exhibit interesting behaviors. The present study describes the possible nonexistence of Borromean binding as well as Efimov states. The possible existence of quasi-bound resonances states for the negatively charged screened Ps-like ions is briefly discussed.

Instantons, colloids and convergence of the 1/N expansion for the homogeneous electron gas

We investigate non-perturbative corrections to the large N expansion of the homogeneous electron gas. These are associated with instanton solutions to the effective action of the plasmon field. We show that, although the large field behavior of that action dominates the quadratic bare Coulomb term, there are no solutions at large field, and consequently none at large density. We argue that solutions would exist at low density if the large N theory had a Wigner crystal (WC) phase. However, we argue that this is not the case. Together with the implied convergence of the large N expansion, this implies that the homogeneous electron gas with N component spins and a Coulomb interaction scaling like 1∕N can only have a WC phase below a curve in the plane of N and density, which asymptotes to zero density at infinite N. We argue that for systems with a semi-classical expansion for order parameter dynamics, and a first order quantum transition between fluid and crystal phases, there are instantons associated with the decays of meta-stable fluid and crystal phases in the appropriate regions of the phase diagram. We argue that the crystal will decay into one or more colloidal or bubble phases (Kivelson and Spivak, 2006) rather than directly into the fluid. It is possible that the bubble phases remain stable all the way to the density where the crystal solution disappears. The bubbles of fluid will expand as the density is raised and gradually convert the system into a fluid filled with chunks of crystal. The transition to a translationally invariant phase is likely to be second order. Unfortunately, the HEG does not have a crystal phase at large N, where these semi-classical ideas could be examined in detail. We suggest that the evidence for negative dielectric function at intermediate densities for N=2 is an indicator of this second order transition. While the infinite N limit does not have a negative dielectric function at any density, it is possible that the closed large N equation for the plasmon two point function, derived in Banks (2018) might capture at least the qualitative features of the second order transition.

Charged impurity scattering in two-dimensional materials with ring-shaped valence bands: GaS, GaSe, InS, and InSe

The singular density of states and the two Fermi wavevectors resulting from a ring-shaped or "Mexican hat" valence band give rise to unique trends in the charged impurity scattering rates and charged impurity limited mobilities. Ring shaped valence bands are common features of many monolayer and few-layer two-dimensional materials including the III-VI materials GaS, GaSe, InS, and InSe. The wavevector dependence of the screening, calculated within the random phase approximation, is so strong that it is the dominant factor determining the overall trends of the scattering rates and mobilities with respect to temperature and hole density. Charged impurities placed on the substrate and in the 2D channel are considered. The different wavevector dependencies of the bare Coulomb potentials alter the temperature dependence of the mobilities. Moving the charged impurities 5 $\AA$ from the center of the channel to the substrate increases the mobility by an order of magnitude.

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.

Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory

Strong electronic correlations pose one of the biggest challenges to solid state theory. We review recently developed methods that address this problem by starting with the local, eminently important correlations of dynamical mean field theory (DMFT). On top of this, non-local correlations on all length scales are generated through Feynman diagrams, with a local two-particle vertex instead of the bare Coulomb interaction as a building block. With these diagrammatic extensions of DMFT long-range charge-, magnetic-, and superconducting fluctuations as well as (quantum) criticality can be addressed in strongly correlated electron systems. We provide an overview of the successes and results achieved---hitherto mainly for model Hamiltonians---and outline future prospects for realistic material calculations.

Many-body perturbation theory and non-perturbative approaches: screened interaction as the key ingredient

Many-body perturbation theory is often formulated in terms of an expansion in the dressed instead of the bare Green’s function, and in the screened instead of the bare Coulomb interaction. However, screening can be calculated on different levels of approximation, and it is important to define what is the most appropriate choice. We explore this question by studying a zero-dimensional model (so called ‘one-point model’) that retains the structure of the full equations. We study both linear and non-linear response approximations to the screening. We find that an expansion in terms of the screening in the random phase approximation is the most promising way for an application in real systems. Moreover, by making use of the nonperturbative features of the Kadanoff–Baym equation for the one-body Green’s function, we obtain an approximate solution in our model that is very promising, although its applicability to real systems has still to be explored.

Critical screening in the one- and two-electron Yukawa atoms

The one- and two-electron Yukawa atoms, also referred to as the Debye-H\uckel or screened Coulomb atoms, have been topics of considerable interest both for intrinsic reasons and because of their relevance to terrestrial and astrophysical plasmas. At sufficiently high screening the one-electron Yukawa atom ceases to be bound. Some calculations appeared to suggest that as the screening increases in the ground state of the two-electron Yukawa atom (in which both the one-particle attraction and the interparticle repulsion are screened) the two electrons are detached simultaneously, at the same screening constant at which the one-electron atom becomes unbound. Our results rule this scenario out, offering an alternative that is not less interesting. In particular, it is found that for $Zl1$ a mild amount of screening actually increases the binding energy of the second electron. At the nuclear charge ${Z}_{c}\ensuremath{\approx}0.911028...$, at which the bare Coulomb two-electron atom becomes unbound, and even over a range of lower nuclear charges, an appropriate amount of screening gives rise to a bound two-electron system.

Improved electronic structure and magnetic exchange interactions in transition metal oxides

We discuss the application of the Agapito Curtarolo and Buongiorno Nardelli (ACBN0) pseudo-hybrid Hubbard density functional to several transition metal oxides. For simple binary metal oxides, ACBN0 is found to be a fast, reasonably accurate and parameter-free alternative to traditional DFT + U and hybrid exact exchange methods. In ACBN0, the Hubbard energy of DFT + U is calculated via the direct evaluation of the local Coulomb and exchange integrals in which the screening of the bare Coulomb potential is accounted for by a renormalization of the density matrix. We demonstrate the success of the ACBN0 approach for the electronic properties of a series technologically relevant mono-oxides (MnO, CoO, NiO, FeO, both at equilibrium and under pressure). We also present results on two mixed valence compounds, Co3O4 and Mn3O4. Our results for these binary oxides and all the materials we have investigated, obtained at the computational cost of a standard LDA/PBE calculation, are in excellent agreement with hybrid functionals, the GW approximation and experimental measurements.