Theory Of Electron Gas Research Articles

First step toward a parameter-free, nonlocal kinetic energy density functional for semiconductors and simple metals.

The accuracy of orbital-free density functional theory depends on the approximations made for a Kinetic Energy (KE) functional. Until now, the most accurate KEDFs are based on non-local kernels constructed from the linear response theory of homogeneous electron gas. In this work, we explore beyond the HEG by employing a more general kernel based on the jellium-with-gap model (JGM). The proposed functional incorporates several new features, such as (i) having the correct low momentum(q) limit of the response function for metals and semiconductors without any modeling term, (ii) the underlying kernel is density-independent, and most importantly, (iii) parameter-free. The accuracy and efficiency of the proposed JGM NL-KEDF have been demonstrated for several semiconductors and metals. The encouraging results indicate the utility and predictive power of the JGM kernel for NL KEDF developments. This approach is also physically appealing and practically useful as we have presented a general formalism to incorporate the gap kernel in all existing Lindhard-based functionals.

Free electron gas in cavity quantum electrodynamics

Cavity modification of material properties and phenomena is a novel research field largely motivated by the advances in strong light-matter interactions. Despite this progress, exact solutions for extended systems strongly coupled to the photon field are not available, and both theory and experiments rely mainly on finite-system models. Therefore, a paradigmatic example of an exactly solvable extended system in a cavity becomes highly desirable. To fill this gap we revisit Sommerfeld's theory of the free electron gas in cavity quantum electrodynamics. We solve this system analytically in the long-wavelength limit for an arbitrary number of noninteracting electrons, and we demonstrate that the electron-photon ground state is a Fermi liquid which contains virtual photons. In contrast to models of finite systems, no ground state exists if the diamagentic ${\mathbf{A}}^{2}$ term is omitted. Further, by performing linear response we show that the cavity field induces plasmon-polariton excitations and modifies the optical and the DC conductivity of the electron gas. Our exact solution allows us to consider the thermodynamic limit for both electrons and photons by constructing an effective quantum field theory. The continuum of modes leads to a many-body renormalization of the electron mass, which modifies the fermionic quasiparticle excitations of the Fermi liquid and the Wigner-Seitz radius of the interacting electron gas. Last, we show how the matter-modified photon field leads to a repulsive Casimir force and how the continuum of modes introduces dissipation into the light-matter system. Several of the presented findings should be experimentally accessible.

The kinetic inductance of single-walled carbon nanotube metal type

The results of theoretical studies of the kinetic inductance Lk metallic single-walled carbon nanotube type, taking into account the electron-electron interaction in the approximation of a right circular cylinder are presented. The system under consideration is a cylindrically symmetric potential well with a final height of the wall. As part of the response of the theory of two-dimensional electron gas in the external electromagnetic disturbance obtained in the form of kinetic inductance depending on the nanotube diameter, frequency and intensity of the radiation. Established that Lk value increases with increasing frequency, and decreases with increasing radiation intensity.

To the Theory of Inhomogeneous Electron Gas

Nonrigorous character of the density-functional theory for inhomogeneous electron gas based on the hypothesis assuming the existence of a universal density functional is demonstrated. A single-particle density matrix must be determined to calculate the ground-state energy of a finite system with a finite number of electrons. A single-particle Green function can be used to unambiguously determine the ground-state energy of an inhomogeneous electron system that satisfies the thermodynamic limit.

On the Problem of Universal Density Functional

A performed analysis shows that the density functional theory for the inhomogeneous electron gas, which is based on the hypothesis of the existence of the density functional for the external field potential is incorrect. This means that the density functional theory is not an ab initio theory.

Density Functional Theory for Electron Gas and for Jellium.

Density functional theory relies on universal functionals characteristic of a given system. Those functionals in general are different for electron gas and for jellium (electron gas with a uniform background). However, jellium is frequently used to construct approximate functionals for an electron gas (e.g., local density approximation and gradient expansions). The precise relationship of the exact functionals for the two systems is addressed here. In particular, it is shown that the exchange-correlation functionals for the inhomogeneous electron gas and inhomogeneous jellium are the same. This justifies theoretical and quantum Monte Carlo simulation studies of jellium to guide the construction of functionals for an electron gas. Related issues of the thermodynamic limit are noted as well.

Geometric Derivation of the Stress Tensor of the Homogeneous Electron Gas

The foundation of many approximations in time-dependent density functional theory (TDDFT) lies in the theory of the homogeneous electron gas. However, unlike the ground-state DFT, in which the exchange-correlation potential of the homogeneous electron gas is known exactly via the quantum Monte Carlo calculation, the time-dependent or frequency-dependent dynamical potential of the homogeneous electron gas has not been known exactly, due to the absence of a similar variational principle for excited states. In this work, we present a simple geometric derivation of the time-dependent dynamical exchange-correlation potential for the homogeneous system. With this derivation, the dynamical potential can be expressed in terms of the stress tensor, offering an alternative to calculate the bulk and shear moduli, two key input quantities in TDDFT.

Arnold Sommerfeld and Condensed Matter Physics

Arnold Sommerfeld (1868–1951), one of the founders of modern theoretical physics and a pioneer of quantum theory, was no condensed matter physicist. He nevertheless played a crucial role for the history of the field. Besides his important contributions to the study of condensed matter systems, among which his seminal electron gas theory of metallic conduction probably stands out, he influenced the field through his very approach to science, through his way of “doing” physics. Sommerfeld's specific style permeated not only his research but also his teaching and his promoting of physics. This has had a lasting influence on the practices of physicists to this day, and not only, but importantly, on those of condensed matter physicists. This article aims to provide a concise account of Sommerfeld's influence on the study of condensed matter systems, with regard to both his research and his practice.

Static polarizability in a combined model

In the framework of the theory of inhomogeneous electron gas, we consider a model to calculate the static multipole polarizability. The analysis shows the possibility of the specific dependence of the electron density perturbation (potential) of an atom in a weak external electrostatic field.

Новая теория электронного газа в магнитном поле и задачи для теории и эксперимента

Новая теория электронного газа в магнитном поле и задачи для теории и эксперимента

Static polarizability of condensed particles

Within the inhomogeneous electron gas theory, a model is considered for calculations of static polarizability of matter. The analysis confirms the high accuracy of the new model. Among the main advantages of the model are its simplicity and physical transparency, as well as lack of computational problems.

Temperature- and thickness-dependent electrical conductivity of few-layer graphene and graphene nanosheets

We established a calculation model of the conductivity of multilayer graphene based on Boltzmann transport equation and 2D electron gas theory. Numerical simulations show that the conductivities of few-layer graphene and graphene nanosheets are reduced when thickness is increased. The reduction rate decreases for micron-range thicknesses and remains constant thereafter. Moreover, the conductivity increases with the increase in temperature, in which the increase rate declines as temperature increases. Higher thickness exhibits a more obvious temperature effect on conductivity. Such effect also increases with the increase in temperature.

Dipolar quantum electrodynamics theory of the three-dimensional electron gas

We provide a description of the interaction between light and a three-dimensional electron gas in the framework of the Power-Zienau-Wooly (PZW) formulation of the quantum electrodynamics. The existence of the collective plasmon and plasmon-polariton modes of the gas appears as a consequence of the general properties of the PZW Hamiltonian. Our description enables a fully microscopic theory of the surface plasmon-polariton excitations, based on a quantum Hamiltonian that is free from any additional hypothesis regarding the material dispersion. This theory can therefore be applied to study the quantum optical properties of plasmon and surface plasmon waves.

Theory of the SrTiO3surface state two-dimensional electron gas

We present a theory of the quasi two-dimensional electron gas (2DEG) systems which appear near the surface of SrTiO$_3$ when a large external electric field attracts carriers to the surface. We find that non-linear and non-local screening by the strongly polarizable SrTiO$_3$ lattice plays an essential role in determining 2DEG properties. The electronic structure always includes weakly bound bulk-like bands that extend over many SrTiO$_3$ layers. At 2D carrier-densities exceeding $\sim 10^{14} {\rm cm}^{-2}$ tightly bound bands emerge that are confined within a few layers of the surface.

New Al0.25Ga0.75N/GaN HEMTs structure with the partial silicon doping

By applying the theory of two-dimensional electron gas (2DEG) formed in the AlGaN/GaN high electron mobility transistors, two 2DEG concentration regions are realised by doping partial silicon into the AlGaN layer for the first time. A new electric field peak is introduced in the surface electric field by the electric field modulation effect due to the partial silicon positive charge. The high electric fields near the gate and drain electrodes are decreased effectively, and the surface electric field is uniform. The proposed structure with the partial silicon doping is better than the conventional structures with the electric field plate near the drain, which is due to the absence of the adding capacitance. The breakdown voltage is improved from 308 V for the conventional structure to 400 V for the proposed one resulting from the uniform surface electric field.

Simple model of bulk and surface excitation effects to inelastic scattering in low-energy electron beam irradiation of multi-walled carbon nanotubes

The effect of bulk and surface excitations to inelastic scattering in low-energy electron beam irradiation of multi-walled carbon nanotubes (MWNTs) is studied using the dielectric formalism. Calculations are based on a semiempirical dielectric response function for MWCNTs determined by means of a many-pole plasmon model with parameters adjusted to available experimental spectroscopic data under theoretical sum-rule constrains. Finite-size effects are considered in the context of electron gas theory via a boundary correction term in the plasmon dispersion relations, thus, allowing a more realistic extrapolation of the electronic excitation spectrum over the whole energy-momentum plane. Energy-loss differential and total inelastic scattering cross sections as a function of electron energy and distance from the surface, valid over the energy range ∼50–30,000 eV, are calculated with the individual contribution of bulk and surface excitations separated and analyzed for the case of normally incident and escaping electrons. The sensitivity of the results to the various approximations for the spatial dispersion of the electronic excitations is quantified. Surface excitations are shown to have a strong influence upon the shape and intensity of the energy-loss differential cross section in the near surface region whereas the general notion of a spatially invariant inelastic mean free path inside the material is found to be of good approximation.

Constraints of reduced density-matrix functional theory for the two-dimensional homogeneous electron gas

Reduced density-matrix functional theory (RDMFT) has become an appealing alternative to density-functional theory to describe electronic properties of highly-correlated systems. Here we derive exact conditions for the suitability of RDMFT to describe the two-dimensional homogeneous electron gas, which is the base system for, e.g., semiconductor quantum dots and quantum Hall devices. Following the method of Cioslowski and Pernal [J. Chem. Phys. {\bf 111}, 3396 (1999)] we focus on the properties of power functionals of the form $f(n,n')=(n n')^\alpha$ for the scaling function in the exchange-correlation energy. We show that in order to have stable and analytic solutions, and for $f$ to satisfy the homogeneous scaling constraint, the power is restricted to $1/4 \leq \alpha \leq 3/4$. Applying a reasonable ansatz for the momentum distribution and the lower bound for the exchange-correlation energy tightens the physical regime further to $0.64 \lesssim \alpha \leq 0.75$.

Inelastic scattering of low-energy electrons in liquid water computed from optical-data models of the Bethe surface

Purpose: We provide a short overview of optical-data models for the description of inelastic scattering of low-energy electrons (10–10,000 eV) in liquid water. The effect on the inelastic scattering cross section due to different optical data and extension algorithms is examined with emphasis on some recent developments.Materials and methods: The optical-data method whereby experimental optical data and theoretical extension algorithms are used to describe the dependence of the dielectric response function on energy- and momentum-transfer and obtain the Bethe surface of the material, currently represents the most used method for computing the inelastic scattering of low-energy electrons in condensed media. Two sets of experimental optical data for liquid water obtained from reflectance and inelastic X-ray scattering spectroscopy, respectively, and the extension algorithms of Ritchie, Penn, and Ashley are examined. Recent developments are discussed along with the role of corrections to the random phase approximation (RPA) of electron gas theory. Results: The inelastic scattering cross section in the energy range 200–10,000 eV was found to be rather insensitive (to within 10%) to the choice of optical data or the extension algorithm. In contrast, differences between model calculations increase rapidly below 200 eV with the influence of the extension algorithm being dominant.Conclusion: The choice of the extension algorithm used to extrapolate optical data to finite momentum transfer and obtain the Bethe surface is crucial in modelling the inelastic scattering of electrons with energies below 200 eV. A new set of measurements on the dielectric response function of liquid water beyond the optical limit and the development of extension algorithms that will go beyond RPA by considering the effect of (short-range) electron exchange and correlation should be of some priority.

Atomic number dependences of atomic radii and ionization potentials according to “Multicomponent Electron Gas” theory

Multicomponent electron gas theory is applied to describe the chemically significant properties of atoms, such as atomic radii and ionization potentials. The dependence of these characteristics on the atomic number is described.

Electron inelastic mean free paths in biological matter based on dielectric theory and local-field corrections

The inelastic mean free path (IMFP) of electrons with energies up to a few keV is calculated from the dielectric electron-gas theory for densities corresponding to those of biological matter. The effect of the many-body local-field correction on the Lindhard dielectric response function is examined using some of the available analytical approximations to its static limit. We have tested the performance of several Hubbard-type local-field corrections along with the formula proposed by Corradini and co-workers [M. Corradini, R. Del Sole, G. Onida, M. Palumno, Phys. Rev. B 57 (1998) 14569] which is extensively used in connection with the exchange-correlation kernel of time-dependent density functional theory. It is shown that the Lindhard dielectric function provides reasonable estimates of electron IMFPs below about 50 eV, where the majority of semi-empirical dielectric calculations based on the extended-optical-data methodology fail. The use of LFC results in a sizeable reduction of the IMFP which, at low energies, may reach ∼20%.