Local Field Correction Research Articles

Ionized impurity scattering in quantum wells and quantum wires

Low-field mobility for scattering of electrons by ionized impurities is calculated in quantum wells and quantum wires. Analytical expressions for mobility are obtained on the basis of the quantum-kinetic approach using the quantum mechanical formalism of the dielectric function for non-interacting and interacting electrons. If the kinetic energy of electrons is much higher than their inter-particle potential energy, the electron system remains qualitatively similar to a non-interacting electron gas. The Lindhard dielectric function is used to calculate the mobility and screening factor of non-interacting electrons. If the potential energy of electrons is close to or prevails over their kinetic energy, the electron system displays a collective behavior similar to an electron liquid. In this case, electrons are considered interacting. To calculate the mobility of the interacting electrons, we have used the static local-field correction factor to the electron dielectric function. Analytical dependences of the electron mobility on dimensionality of the electron system, sizes of the quantum structures in the confining directions, temperature, forms of confining potential, electron density, and material parameters are obtained. The quantum confinement is modeled by triangular and rectangular confining potentials. The results of calculations are compared with the known experimental data.

Coulomb drag study in graphene/GaAs bilayer system with the effect of local field correction and dielectric medium

The drag resistivity is measured numerically for electron-electron (e-e) and electron-hole (e-h) coupled layer system composed of single layer graphene and two-dimensional (2D) GaAs layer separated by a barrier. The system is studied within the model of random phase approximation (RPA) and taking into account the static local field correction (LFC) and layer thickness effects in the Ballistic/Boltzmann regime. We have shown analytical expressions of non-linear susceptibility function and effective interlayer Coulomb interaction for non homogeneous dielectric environment at low temperature, high density and large interlayer separation limit. Exchange and correlation effects enhanced the drag resistivity by considering the static local field correction. Width of the layer and interlayer distance dependent local form factors (LFF) are obtained from the solution of the Poisson equation for a multi-layer dielectric medium. The effects of LFC and LFF are the function of bare inter- and intra-layer potential, which enhances the drag resistivity compare to simply measured RPA results. Enhanced drag resistivity also measured for e-h bilayer system where the hole layer is considered for 2D GaAs (drag layer), cause of larger effective mass of hole compare to the electron. Similarly, e-e and e-h bilayer system measured the enhanced drag resistivity due to LFC effects.

Dynamic properties of the warm dense electron gas based on ab initio path integral Monte Carlo simulations

There is growing interest in warm dense matter (WDM) -- an exotic state on the border between condensed matter and plasmas. Due to the simultaneous importance of quantum and correlation effects WDM is complicated to treat theoretically. A key role has been played by \textit{ab initio} path integral Monte Carlo (PIMC) simulations, and recently extensive results for thermodynamic quantities have been obtained. The first extension of PIMC simulations to the dynamic structure factor of the uniform electron gas were reported by Dornheim \textit{et al.} [Phys. Rev. Lett. \textbf{121}, 255001 (2018)]. This was based on an accurate reconstruction of the dynamic local field correction. Here we extend this concept to other dynamical quantities of the warm dense electron gas including the dynamic susceptibility, the dielectric function and the conductivity.

Study of collective mode excitations in Zr41Ti14Cu12.5Be22.5Fe10 bulk metallic glass

Abstract The collective mode excitations of Zr41Ti14Cu12.5Be22.5Fe10 bulk metallic glass (BMG) have been theoretically studied at room temperature by applying pseudopotential technique. A well-known Shaw’s optimized constant core model pseudopotential with five different forms of local field correction functions given by Hartree (H), Taylor (T), Ichimaru-Utsumi (IU), Farid et al. (F) and Sarkar et al. (S) are used to study the screening effects on the aforementioned work. The phonon dispersion curves (PDCs) are computed by using Hubbard-Beeby (HB) theoretical approach. While, elastic and thermodynamic properties are theoretically calculated from the elastic limit of the phonon dispersion curve. Such properties compared well with available data in the literature and are found qualitative agreement with them.

Ab initio path integral monte carlo simulation of the uniform electron gas in the high energy density regime

The response of the uniform electron gas (UEG) to an external perturbation is of paramount importance for many applications. Recently, highly accurate results for the static density response function and the corresponding local field correction have been provided both for warm dense matter [2019 J. Chem. Phys. 151 194104] and strongly coupled electron liquid [2020 Phys. Rev. B 101 045129] conditions based on exact ab initio path integral Monte Carlo (PIMC) simulations. In the present work, we further complete our current description of the UEG by exploring the high energy density regime, which is relevant for, e.g. astrophysical applications and inertial confinement fusion experiments. To this end, we present extensive new PIMC results for the static density response in the range of 0.05 ≤ rs≤ 0.5 and 0.85 ≤ θ ≤ 8. These data are subsequently used to benchmark the accuracy of the widely used random phase approximation and the dielectric theory by Singwi, Tosi, Land, and Sjölander (STLS). Moreover, we compare our results to configuration PIMC data where they are available and find perfect agreement with a relative accuracy of 0.001 − 0.01%. All PIMC data are available online.

Transport Properties of a GaAs/InGaAs/GaAs Quantum Well: Temperature, Magnetic Field and Many-body Effects

We investigate the zero and finite temperature transport properties of a quasi-two-dimensional electron gas in a GaAs/InGaAs/GaAs quantum well under a magnetic field, taking into account many-body effects via a local-field correction. We consider the surface roughness, roughness-induced piezoelectric, remote charged impurity and homogenous background charged impurity scattering. The effects of the quantum well width, carrier density, temperature and local-field correction on resistance ratio are investigated. We also consider the dependence of the total mobility on the multiple scattering effect.

Dynamic correlation effects on correlational properties of finite-temperature quasi-one-dimensional electron gas

We have studied correlational properties of quasi-one-dimensional electron gas at finite temperature T by incorporating the dynamics of electron correlations within the quantum version of the self-consistent mean-field approach of Singwi, Tosi, Land, and Sjölander. Static structure factor, pair-correlation function, static density susceptibility, excess kinetic energy, and free correlation energy are calculated covering a wide range of temperature and electron number density. As at absolute zero temperature, the inclusion of dynamics of correlations results in stronger spatial electron correlations, with a pronounced peak in the static structure factor at wave vector q ∼ 3.5kF, which grows further with decreasing electron density. Below a critical density, the static density susceptibility seems to diverge at this value of q, signaling a transition from liquid to the Wigner crystal state-a prediction in qualitative agreement with recent simulations and experiment. However, thermal effects tend to impede crystallization with the consequence that the critical density decreases significantly with rising T. On the other hand, the pair-correlation function at short range exhibits a non-monotonic dependence on T, initially becoming somewhat stronger with rising T and then weakening continuously above a sufficiently high T. The calculated free correlation energy shows a noticeable dependence on T, with its magnitude increasing with increase in T. Further, we have looked into the effect of temperature on the frequency-dependence of dynamic local-field correction factor and the plasmon dispersion. It is found that with rising T the dynamics of correlations weakens, and the plasmon frequency exhibits a blue shift. Wherever interesting, we have compared our results with the lower-order approximate calculations and zero-T quantum Monte Carlo simulations.

Ion energy-loss characteristics and friction in a free-electron gas at warm dense matter and nonideal dense plasma conditions.

We investigate the energy-loss characteristics of an ion in warm dense matter (WDM) and dense plasmas concentrating on the influence of electronic correlations. The basis for our analysis is a recently developed ab initio quantum Monte Carlo- (QMC) based machine learning representation of the static local field correction (LFC) [Dornheim et al., J. Chem. Phys. 151, 194104 (2019)JCPSA60021-960610.1063/1.5123013], which provides an accurate description of the dynamical density response function of the electron gas at the considered parameters. We focus on the polarization-induced stopping power due to free electrons, the friction function, and the straggling rate. In addition, we compute the friction coefficient which constitutes a key quantity for the adequate Langevin dynamics simulation of ions. Considering typical experimental WDM parameters with partially degenerate electrons, we find that the friction coefficient is of the order of γ/ω_{pi}=0.01, where ω_{pi} is the ionic plasma frequency. This analysis is performed by comparing QMC-based data to results from the random-phase approximation (RPA), the Mermin dielectric function, and the Singwi-Tosi-Land-Sjölander (STLS) approximation. It is revealed that the widely used relaxation time approximation (Mermin dielectric function) has severe limitations regarding the description of the energy loss of ions in a correlated partially degenerate electrons gas. Moreover, by comparing QMC-based data with the results obtained using STLS, we find that the ion energy-loss properties are not sensitive to the inaccuracy of the static local field correction (LFC) at large wave numbers, k/k_{F}>2 (with k_{F} being the Fermi wave number), but that a correct description of the static LFC at k/k_{F}≲1.5 is important.

Ab initio simulation of warm dense matter

Warm dense matter (WDM)—an exotic state of highly compressed matter—has attracted increased interest in recent years in astrophysics and for dense laboratory systems. At the same time, this state is extremely difficult to treat theoretically. This is due to the simultaneous appearance of quantum degeneracy, Coulomb correlations, and thermal effects, as well as the overlap of plasma and condensed phases. Recent breakthroughs are due to the successful application of density functional theory (DFT) methods which, however, often lack the necessary accuracy and predictive capability for WDM applications. The situation has changed with the availability of the first ab initio data for the exchange–correlation free energy of the warm dense uniform electron gas (UEG) that were obtained by quantum Monte Carlo (QMC) simulations; for recent reviews, see Dornheim et al., Phys. Plasmas 24, 056303 (2017) and Phys. Rep. 744, 1–86 (2018). In the present article, we review recent further progress in QMC simulations of the warm dense UEG: namely, ab initio results for the static local field correction G(q) and for the dynamic structure factor S(q,ω). These data are of key relevance for comparison with x-ray scattering experiments at free electron laser facilities and for the improvement of theoretical models. In the second part of this paper, we discuss the simulations of WDM out of equilibrium. The theoretical approaches include Born-Oppenheimer molecular dynamics, quantum kinetic theory, time-dependent DFT, and hydrodynamics. Here, we analyze the strengths and limitations of these methods and argue that progress in WDM simulations will require a suitable combination of all methods. A particular role might be played by quantum hydrodynamics, and we concentrate on problems, recent progress, and possible improvements of this method.

Spin decoherence in inhomogeneous media

A Green’s function formalism for describing the decoherence of a ‘central spin’ in inhomogeneous media is developed. By embedding the ‘central spin’ in a background medium and performing real-cavity, local-field corrections on the macroscopic fields at the location of the ‘central spin’ one can show that the Green’s function splits up into two main contributions, a contribution that is related to the bulk properties of the background medium and a contribution that is related inhomogeneities within the background medium. As an example, the coherence time of a shallow NV center in diamond close to a planar interface, both in the absence and presence of surface spins, is computed. It is found that the coherence time of the NV center increases as it moves away from the interface and, at distances greater than ≈1 nm, the interaction with the interface is negligible with the main source of decoherence coming from the interaction with the surface spins. Above ≈50 nm the interaction with the surface spins is also negligible and one recovers the bulk coherence time.

Strongly coupled electron liquid: Ab initio path integral Monte Carlo simulations and dielectric theories

The strongly coupled electron liquid provides a unique opportunity to study the complex interplay of strong coupling with quantum degeneracy effects and thermal excitations. To this end, we carry out extensive \textit{ab initio} path integral Monte Carlo (PIMC) simulations to compute the static structure factor, interaction energy, density response function, and the corresponding static local field correction in the range of $20\leq r_s \leq 100$ and $0.5\leq \theta\leq 4$. We subsequently compare these data to several dielectric approximations, and find that different schemes are capable to reproduce different features of the PIMC results at certain parameters. Moreover, we provide a comprehensive data table of interaction energies and compare those to two recent parametrizations of the exchange-correlation free energy, where they are available. Finally, we briefly touch upon the possibility of a charge-density wave. The present study is complementary to previous investigations of the uniform electron gas in the warm dense matter regime and, thus, further completes our current picture of this fundamental model system at finite temperature. All PIMC data are available online.

The scattering time of electrons in a GaAs/InGaAs/GaAs quantum well including temperature and exchange-correlation effects

The ratio of the scattering and single-particle relaxation time of a quasi-two-dimensional electron gas (Q2DEG) in a finite lattice-mismatched GaAs/InGaAs/GaAs quantum well was investigate at zero and finite temperatures, taking into account the exchange-correlation effects via a local-field correction with three approximations for the LFC, G = 0, GH, and GGA. We studied the dependence of the surface roughness, roughness-induced piezoelectric, remote and homogenous background charged impurity scattering on the carrier density and quantum well width. In the case of zero temperature and Hubbard local-field correction our results reduced to those of different theoretical calculations. At low density, the exchange-correlation effects depend strongly on the ratio τt/τs. While at high density many-body effects due to exchange and correlation considerably modified the ratio of the scattering and single-particle relaxation time. We found that, for densities and temperatures considered T = 0,3TF in this study, the temperature affected weakly on the time ratio for four scatterings. Furthermore, with the change of quantum well width, the effect of LFC and temperatures act on the ratio τt/τs are negligible for the roughness-induced piezoelectric and remote charged impurity scattering, and are notable for the surface roughness and homogenous background charged impurity scattering.

The static local field correction of the warm dense electron gas: An ab initio path integral Monte Carlo study and machine learning representation.

The study of matter at extreme densities and temperatures as they occur in astrophysical objects and state-of-the-art experiments with high-intensity lasers is of high current interest for many applications. While no overarching theory for this regime exists, accurate data for the density response of correlated electrons to an external perturbation are of paramount importance. In this context, the key quantity is given by the local field correction (LFC), which provides a wave-vector resolved description of exchange-correlation effects. In this work, we present extensive new path integral Monte Carlo (PIMC) results for the static LFC of the uniform electron gas, which are subsequently used to train a fully connected deep neural network. This allows us to present a representation of the LFC with respect to continuous wave-vectors, densities, and temperatures covering the entire warm dense matter regime. Both the PIMC data and neural-net results are available online. Moreover, we expect the presented combination of ab initio calculations with machine-learning methods to be a promising strategy for many applications.

Ab initio simulations and measurements of the free-free opacity in aluminum.

The free-free opacity in dense systems is a property that both tests our fundamental understanding of correlated many-body systems, and is needed to understand the radiative properties of high energy-density plasmas. Despite its importance, predictive calculations of the free-free opacity remain challenging even in the condensed matter phase for simple metals. Here we show how the free-free opacity can be modelled at finite-temperatures via time-dependent density functional theory, and illustrate the importance of including local field corrections, core polarization, and self-energy corrections. Our calculations for ground-state Al are shown to agree well with experimental opacity measurements performed on the Artemis laser facility across a wide range of extreme ultraviolet wavelengths. We extend our calculations across the melt to the warm-dense matter regime, finding good agreement with advanced plasma models based on inverse bremsstrahlung at temperatures above 10eV.

On the potential as nonlinear optical material of a new chalcone derivative and its crystal and topological analysis

We report a study of the structural and the linear and nonlinear optical and electrical properties of a new chalcone. Using the Møller-Plesset Perturbation and the Density Functional approaches, the dipole moment, linear polarizability and second hyperpolarizabilities were calculated in static and dynamic electric fields. The supermolecule approach was used to simulate the crystalline environment of our crystal and the linear refractive index. Lorentz local field correction factor and third order macroscopic susceptibility were calculated, and the effects of solvent media on the non-linear optical properties are also taken into account through the Polarizable Continuum Model. This chalcone is almost planar, except for slight rotations in its open-chain which allows electron delocalization. This is also confirmed by an intramolecular hydrogen bond formed between the carbonyl and amine groups. Interestingly, a good third order macroscopic susceptibility value of 13.31 × 10−22m2V−2 was calculated, which is even higher than those reported for related chalcone derivatives.

Effect of the Addition of Pb3O4 and TiO2 on the Optical Properties of Er3+/Yb3+:TeO2-WO3 Glasses.

Heavy metal oxide tungstate-based tellurite glasses TeO2–WO3 (TW) containing Er3+/Yb3+ ions have been prepared by the melting and quenching method. The optical absorption and upconversion (UC) emission studies for the doped/codoped glasses have been performed. The effect of the addition of Pb3O4 and TiO2 to the Er3+/Yb3+:TW glass on its physical properties, optical absorption, and UC emission spectra under 980 nm/808 nm excitations has been studied. A significant enhancement in the UC emission intensity lying in the green and red region has been observed on introducing Pb3O4 and TiO2 into the Er3+/Yb3+:TW glass. The improvement in the UC emission intensity and full width at half maximum of the bands have been explained on the basis of energy transfer, local field correction factor, and Urbach energy. The non-color tunability in the color emitted from the prepared Er3+/Yb3+:TWPTi glass upon near-infrared (NIR) excitation at different pump power has been reported. Also, the color-correlated temperature and color purity have been measured under both NIR excitations.

Analytical approximation to the complex refractive index of nanofluids with extended applicability.

Currently, there are available a few simple analytical approximations to the complex effective refractive index that may be used for nanofluids. Namely, the Maxwell Garnett mixing formula with scattering corrections, the Maxell Garnett Mie approximation, the Foldy-Lax approximation and the small particle limit of the quasi-crystalline approximation. These approximations are valid either for very small nanoparticles (below a few nanometers in radius) or for very dilute nanofluids (below about 1% in particles' volume fractions) and therefore, do not cover the whole domain of particle suspensions referred to as nanofluids. Here we propose a new simple analytical approximation based on local field corrections to the Foldy-Lax approximation. The new mixing formula coincides with the mentioned approximations when they are expected to be valid and provides physically sound predictions when the mentioned approximations are no longer valid, within the realm of nanofluids. We compare predictions of the analytical approximations considered in this work with experimental data published earlier for nanofluids of polystyrene in water.

Reciprocal space approach to effective constitutive parameters of periodic composites

We adopt a technique previously used for crystalline solids to calculate the effective permittivity of periodic nanostructured composites. Our technique, which is based on the reciprocal space representation of a mesoscopic permittivity tensor, allows one to accurately take into account the local field corrections to the effective permittivity of 2D and 3D metamaterials made of lossy anisotropic constituents. To demonstrate the feasibility and to assess the convergence and accuracy of computational procedure used, we consider two 2D geometries for which exact analytical solutions are known (checkerboard geometry and square geometry) and one geometry, for which an exact solution is known in an asymptotic limit (quasi-one-dimensional geometry). It has been shown that the accuracy of the method can be improved when using Keller’ss duality relation.

Calculation of electrical resistivity of Na-based liquid binary alkali alloys

Electrical resistivity, ρ, for Na-based liquid alkali binary alloys namely NaxK1−x, NaxRb1−x, NaxCs1−x and NaxLi1−x are calculated using the extended Ziman's formula developed by Faber and Ziman. Form factor, Vij(q), and partial structure factor, Sij(q), are the main ingredients of this calculation. For Vij(q), we have chosen Bretonnet-Silbert (BS) pseudo-potential with Ichimaru-Utsumi (IU), and Vashishta-Singwi (VS) local field correction functions. For Sij(q), we have chosen linearized Weeks-Chandler-Andersen (LWCA) thermodynamic perturbation theory. From the comparison of the calculated results of ρ with available experimental data and other theoretical values, a good qualitative consistency is found except for liquid NaxLi1−x alloys. We observe that VS local field correction function along with LWCA theory provides much better results than those obtained with IU local field correction near melting point at the liquid state. Calculated results at temperatures far from the melting curve are deviated much from experimental data. Explanation behind this discrepancy requires a further study with more sophisticated theory.

Dispersion forces in inhomogeneous planarly layered media: A one-dimensional model for effective polarizabilities

Dispersion forces such as van der Waals forces between two microscopic particles, the Casimir-Polder forces between a particle and a macroscopic object, or the Casimir force between two dielectric objects are well studied in vacuum. However, in realistic situations the interacting objects are often embedded in an environmental medium. Such a solvent influences the induced dipole interaction. With the framework of macroscopic quantum electrodynamics, these interactions are mediated via an exchange of virtual photons. Via this method the impact of a homogeneous solvent medium can be expressed as local-field corrections leading to excess polarizabilities which have previously been derived for hard boundary conditions. In order to develop a more realistic description, we investigate a one-dimensional analog system illustrating the influence of a continuous dielectric profile.