Free Electron Gas Research Articles

Yb5Rh6Sn18: a valence fluctuating system with ultra-low thermal conductivity.

Yb5Rh6Sn18 crystallizes with a unique structural arrangement [space group P42/nmc, a = 9.6997(4) Å, c = 13.7710(7) Å], which is related with primitive cubic Yb3Rh4Sn13 and body-centered tetragonal (Sn1-xTbx)Tb4Rh6Sn18 types. X-ray absorption spectroscopy showed that Yb atoms exhibit temperature-dependent valence fluctuations (VF) (i.e., intermediate valence state). Its complex mechanism is corroborated by the fact that the well-pronounced maximum in magnetic susceptibility can only be fairly described by the Bickers-Cox-Wilkins model developed for a J = 3/2 multiplet, atypical for Yb ions. Both Hall and Seebeck coefficients revealed a switch of the sign, indicating the change of charge carrier type from electrons to holes between 120 and 220 K. Both these effects together with electrical resistivity and theoretical DFT calculations confirm Yb5Rh6Sn18 to be a metal, which disobeys the free electron gas theory. 'Rattling' motion of Sn1 atoms within the enlarged 16-vertices distorted Frank-Kasper polyhedra, concluded from the specific heat measurements, is argued to be the main reason for the appearance of a phonon resonance behavior, resulting in an ultra-low thermal conductivity in the studied stannide.

Electron confinement-induced plasmonic breakdown in metals.

Plasmon resonance represents the collective oscillation of free electron gas density and enables enhanced light-matter interactions in nanoscale dimensions. Traditionally, the classical Drude model describes plasmonic excitation, wherein plasma frequency exhibits no spatial dispersion. Here, we show conclusive experimental evidence of the breakdown of plasmon resonance and a consequent metal-insulator transition in an ultrathin refractory plasmonic material, hafnium nitride (HfN). Epitaxial HfN thick films exhibit a low-loss and high-quality Drude-like plasmon resonance in the visible spectral range. However, as the film thickness is reduced to nanoscale dimensions, Coulomb interaction among electrons increases because of electron confinement, leading to the spatial dispersion of plasma frequency. With a further decrease in thickness, electrons lose their ability to shield the incident electric field, turning the medium into a dielectric. The observed metal-insulator transition might carry some signatures of Wigner crystallization and indicates that such transdimensional, between 2D and 3D, films can serve as a promising playground to study strongly correlated electron systems.

Two-Term Asymptotics of the Exchange Energy of the Electron Gas on Symmetric Polytopes in the High-Density Limit

We derive a two-term asymptotic expansion for the exchange energy of the free electron gas on strictly tessellating polytopes and fundamental domains of lattices in the thermodynamic limit. This expansion comprises a bulk (volume-dependent) term, the celebrated Dirac exchange, and a novel surface correction stemming from a boundary layer and finite-size effects. Furthermore, we derive analogous two-term asymptotic expansions for semi-local density functionals. By matching the coefficients of these asymptotic expansions, we obtain an integral constraint for semi-local approximations of the exchange energy used in density functional theory.

Classical spin models and basic magnetic interactions on 1/1-approximant crystals

We study classical spin models on the 1/1 Tsai-type approximant lattice using Monte Carlo and mean-field methods. Our aim is to understand whether the phase diagram differences between Gd- and Tb-based approximants can be attributed to anisotropy induced by the crystal-electric field. To address this question, we treat Gd ions as Heisenberg spins and Tb ions as Ising spins. Additionally, we consider the presence of the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction to replicate the experimentally observed correlation between magnetic properties and electron concentration. Surprisingly, our findings show that the transition between ferromagnetic and antiferromagnetic order remains unaltered by the anisotropy, even when accounting for the dipole interaction. We conclude that a more comprehensive model, extending beyond the free-electron gas RKKY interaction, is likely required to fully understand the distinctions between Gd- and Tb-based approximants. Our work represents a systematic exploration of the impact of anisotropy on the ground-state properties of classical spin models in quasicrystal approximants. Published by the American Physical Society 2024

Deeper-band electron contributions to stopping power of silicon for low-energy ions.

This study provides accurate results for the electronic stopping cross sections of H, He, N, and Ne in silicon in low to intermediate energy ranges using various non-perturbative theoretical methods, including real-time time-dependent density functional theory, transport cross section, and induced-density approach. Recent experimental findings [Ntemou et al., Phys. Rev. B 107, 155145 (2023)] revealed discrepancies between the estimates of density functional theory and the observed values. We show that these discrepancies vanish by considering the nonuniform electron density of the deeper silicon bands for ion velocities approaching zero (v → 0). This indicates that mechanisms such as "elevator" and "promotion," which can dynamically excite deeper-band electrons, are active, enabling a localized free-electron gas to emulate ion energy loss, as pointed out by Lim et al. [Phys. Rev. Lett. 116, 043201 (2016)]. The observation and the description of a velocity-proportionality breakdown in electronic stopping cross sections at very low velocities are considered to be a signature of the contributions of deeper-band electrons.

Next-order correction to the Dirac exchange energy of the free electron gas in the thermodynamic limit and generalized gradient approximations

We derive the next order correction to the Dirac exchange energy for the free electron gas in a box with zero boundary conditions in the thermodynamic limit. The correction is of the order of the surface area of the box, and comes from three different contributions: (i) a real-space boundary layer, (ii) a boundary-condition-induced small shift of Fermi momentum and bulk density, and (iii) a long-range electrostatic finite-size correction. Moreover we show that the local density approximation, in addition to capturing the bulk term exactly, also produces a correction of the correct order but not the correct size. Generalized gradient approximation (GGA) corrections are found to be capable of capturing the surface term exactly, provided the gradient enhancement factor satisfies a simple explicit integral constraint. For current GGAs such as B88 and Perdew, Burke and Ernzerhof we find that the new constraint is not satisfied and the size of the surface correction is overestimated by about ten percent. The new constraint might thus be of interest for the design of future exchange functionals.

Scale transformations in model exchange potentials in low energy electron-atom scattering

Model exchange potentials are particularly interesting to account for the indistinguishability between the projectile and target electrons in electron-atom scattering in vacuo and plasma environments. It is well known that their performance is pretty satisfactory in the high energies but also that discrepancies from the results obtained with exact exchange are found toward the zero energy limit. In this article, we examine how well established model exchange potentials based on the free electron gas approach compare to phase shifts calculated considering exchange in exact form. In particular, we show that the Hara and the semiclassical exchange potentials are able to reproduce reference low energy phase shifts through a simple scale transformation, in opposition to the previous approaches where energy dependent corrections to the local momentum were adopted. We provide the scale factors and phase shifts for electron scattering by He, Ne and Ar atoms for k< 1,0 a0−1. Such scaling factors can be determined reproducing the scattering length and the number of s-wave bound states from exact exchange calculations. We also show that the scaling procedure works for electronic densities that present the physically correct asymptotic behavior. The present results are important to the research field, since they form the basis to construction of scattering models based on optical potential approaches.

The sound speed of the relativistic free electron gas

The sound speed of the relativistic free electron gas

Hyperbolic response and low-frequency ultra-flat plasmons in inhomogeneous charge-distributed transition-metal monohalides.

Plasmon, the collective oscillations of free electron gas in materials, determines the long-wavelength excitation spectrum and optical response, are pivotal in the realm of nanophotonics and optoelectronics. In this study, using the first-principles calculations, we systematically investigated the dielectric response and plasmon properties of bulk transition-metal monohalides MXs (M = Zr, Mo; X = Cl, F). Due to the strong electronic anisotropy, MXs exhibit a broadband type-II hyperbolic response and direction-dependent plasmon modes. Particularly, local field effect (LFE) driven by the charge distribution inhomogeneity, significantly modifies the optical response and excitation spectra in MX along the out-of-plane direction. Taking into account LFE, the energy dissipation along the out-of-plane direction is almost completely suppressed, and an ultra-flat and long-lived plasmon mode with a slow group velocity is introduced. This finding reveals the role of charge density in modifying the optical response and excitation behavior, shedding light on potential applications in plasmonics.

The quantum geometric origin of capacitance in insulators

In band insulators, without a Fermi surface, adiabatic transport can exist due to the geometry of the ground state wavefunction. Here we show that for systems driven at a small but finite frequency ω, transport likewise depends sensitively on quantum geometry. We make this statement precise by expressing the Kubo formula for conductivity as the variation of the time-dependent polarization with respect to the applied field. We find that at linear order in frequency, the longitudinal conductivity results from an intrinsic capacitance determined by the ratio of the quantum metric and the spectral gap, establishing a fundamental link between the dielectric response and the quantum metric of insulators. We demonstrate that quantum geometry is responsible for the electronic contribution to the dielectric constant in a wide range of insulators, including the free electron gas in a quantizing magnetic field, for which we show the capacitance is quantized. We also study gapped bands of hBN-aligned twisted bilayer graphene and obstructed atomic insulators such as diamond. In the latter, we find its abnormally large refractive index to have a topological origin.

Static dielectric response and screening in solid state physics: Why dimensionality matters in dielectrics

Textbooks often present the phenomenon of screening within the Thomas–Fermi model for three-dimensional free electron gases, but obtaining the dielectric response function and screening potential for dielectric systems of reduced dimensionality is also of pedagogical interest. In this work, we introduce a simple approach to investigate static screening in dielectric systems in the presence of an impurity charge for different dimensionalities. This approach is applicable to semiconductors and insulators alike. We demonstrate that, in 3D systems, the macroscopic dielectric function in reciprocal space is a constant, while in 2D and 1D systems, it strongly depends on the momentum transferred to the electrons in the dielectric. Through the proposed dielectric screening model, one can also determine binding energies in a hydrogenic model that can be used to describe excitations in real semiconductor systems.

Внезонное поглощение электромагнитного излучения электронами с оптическим фононным участием в сверхрешетках квантовых точек

Physics Institute of Azerbaijan National Academy of Sciences In this paper, we investigate the absorption of electromagnetic radiation by a free electron gas interacting with lattice vibrations in a quantum dot superlattice. It is assumed that the electron gas in the quantum dot superlattice is limited by the anisotropic parabolic potential. The absorption of light by free carriers with the participation of phonons is calculated in the second order of the perturbation theory. When calculating the absorption coefficient, the matrix elements of the electron-photon and electron-phonon interactions (with polar and nonpolar optical phonons) are used. We can expect three possible transitions in the absorption coefficient for electron-polar phonon scattering: (1) a transition due to the size subband levels for only the x direction, (2) a transition due to the size subband levels for only the y direction and (3) a transition due to the size subband levels for both the x direction and the y direction. For electron-nonpolar phonon scattering we can expect оnly one possible transitions in the, the absorption coefficient: a transition due to the size subband levels for both the x direction and the y direction.

Development of a new analytical solution for electronic heat capacity for higher electron temperatures

A new analytical solution has been found for the electronic heat capacity of typical s-band metals. It is valid for high electron temperatures of the order of tens of kK, commonly reached in fs pulsed laser ablation. We have used the density of states (DOS) from the free-electron gas model (FEG) and a special type of function called polylogarithms. From the exact analytical solution, a third order Taylor expansion which works well up to 50kK could be derived. A new term was added to the DOS for d-band metals, which allowed us to find a new semi-analytical solution which predicts accurately the electronic heat capacity of Cu.

High-order cavity coupled plasmon polaritons in resonant cavity-monolayer MoS&lt;sub&gt;2&lt;/sub&gt; system

Compared with graphene, two-dimensional (2D) transition metal sulfides, represented by mono-/few-layer MoS&lt;sub&gt;2&lt;/sub&gt;, have tunable non-zero bandgap, and thus their applications in optoelectronic devices are more advantageous. By using classical electromagnetic theory and finite element method (FEM), we investigate the cavity coupled plasmon polaritons (CCPPs) formed through the coupling between cavity modes in a resonator and plasmons in monolayer MoS&lt;sub&gt;2&lt;/sub&gt;, particularly calculate and verify the properties of the high-order CCPPs. In previous work, it was demonstrated that the substrates, defects, and polycrystalline grains of the CVD grown monolayer MoS&lt;sub&gt;2&lt;/sub&gt; usually induce weak electron localization, which leads to the deviation from the Drude model based on the approximation of free electron gas. Therefore, here we use the Drude-Smith model with characteristic parameters obtained experimentally to describe the optical conductivity of monolayer MoS&lt;sub&gt;2&lt;/sub&gt; in our theoretical calculation and simulation. Then, we not only derive and solve the dispersion equations of the high-order CCPPs, but also verify the existence and analyze the properties of these high-order modes. Specifically, there are three types of CCPPs in the asymmetric cavity-monolayer MoS&lt;sub&gt;2&lt;/sub&gt; system, i.e. the FP-like-modes (FPLMs), the surface-plasmon-like modes (SPLMs), and the quasi-localized modes (QLMs). Among them, the FPLMs and QLMs can support high-order modes whereas the SPLMs only support the fundamental modes. According to our model, we calculate the wave localization properties for the 7th-order and 8th-order FPLM, the 3rd-order and 6th-order QLM, and the SPLM. These theoretical results are in good agreement with the simulation results. Moreover, the effects of weak electron localization are also shown by comparing the field distributions of the CCPPs based on the Drude model with those based on the Drude-Smith model. It is found that weak electron localization can reduce the coupling between the cavity modes and the plasmons in monolayer MoS&lt;sub&gt;2&lt;/sub&gt;. These results can deepen our understanding of the excitation of plasmons in 2D materials as well as the modulation of their properties. Furthermore, the theoretical model can also be extended to other plasmonic systems related to low-dimensional and topological quantum materials.

Linear and nonlinear spin current response of anisotropic spin-orbit coupled systems

We calculate the linear and the second harmonic (SH) spin current response of two anisotropic systems with spin–orbit (SO) interaction. General expressions of wide applicability for the these response functions are first derived for a generic two-band Hamiltonian. The first system is a two-dimensional (2D) electron gas in the presence of Rashba and k-linear Dresselhaus SO couplings. The calculations show how narrow or wide the response spectra can be, what is their overall shape and size, and frequency shiftings, depending on which crystal orientation is selected. The quantitative knowing of this makes possible a comparative study for several orientations, which would allow to select a spectrum with particular characteristic. We find that vanishing linear and second order response tensors are achievable under SU(2) symmetry conditions, characterized by a collinear SO vector field. Additional conditions under which specific tensor components vanish are possible, without having such collinearity. Thus, a proper choice of the growth direction and SO strengths allows to select the polarization of the linear and SH spin currents according to the direction of flowing. The second system is an anisotropic 2D free electron gas with anisotropic Rashba interaction, which has been employed to study the optical conductivity of 2D puckered structures with anisotropic energy bands. The presence of mass anisotropy and an energy gap open several distinct scenarios for the allowed optical interband transitions, which manifest in the linear and SH response contrastingly. The linear response displays only out-of-plane spin polarized currents, while the SH spin currents flow with spin orientation lying parallel to the plane of the system strictly. The models illustrate the possibility of the nonlinear spin Hall effect in systems with SO interaction, under the presence or absence of time-reversal symmetry. The results suggest different ways to manipulate the linear and nonlinear optical generation of spin currents which could find spintronic applications.

Nonlocal Hydrodynamic Model with Viscosive Damping and Generalized Drude–Lorentz Term

The response of plasmonic metal particles to an electromagnetic wave produces significant features at the nanoscale level. Different properties of the internal composition of a metal, such as its ionic background and the free electron gas, begin to manifest more prominently. As the dimensions of the nanostructures decrease, the classical local theory gradually becomes inadequate. Therefore, Maxwell’s equations need to be supplemented with a relationship determining the dynamics of current density which is the essence of nonlocal plasmonic models. In this field of physics, the standard (linearized) hydrodynamic model (HDM) has been widely adopted with great success, serving as the basis for a variety of simulation methods. However, ongoing efforts are also being made to expand and refine it. Recently, the GNOR (general nonlocal optical response) modification of the HDM has been used, with the intention of incorporating the influence of electron gas diffusion. Clearly, from the classical description of fluid dynamics, a close relationship between viscosive damping and diffusion arises. This offers a relevant motivation for introducing the GNOR modification in an alternative manner. The standard HDM and its existing GNOR modification also do not include the influence of interband electron transitions in the conduction band and other phenomena that are part of many refining modifications of the Drude–Lorentz and other models of metal permittivity. In this article, we present a modified version of GNOR-HDM that incorporates the viscosive damping of the electron gas and a generalized Drude–Lorentz term. In the selected simulations, we also introduce Landau damping, which corrects the magnitude of the standard damping constant of the electron gas based on the size of the nanoparticle. We have chosen a spherical particle as a suitable object for testing and comparing HD models and their modifications because it allows the calculation of precise analytical solutions for the interactions and, simultaneously, it is a relatively easily fabricated nanostructure in practice. Our contribution also includes our own analytical method for solving the HDM interaction of a plane wave with a spherical particle. This method forms the core of calculations of the characteristic quantities, such as the extinction cross-sections and the corresponding components of electric fields and current densities.

Average-atom Ziman resistivity calculations in expanded metallic plasmas: Effect of mean ionization definition.

We present calculations of electrical resistivity for expanded boron, aluminum, titanium, and copper plasmas using the Ziman formulation in the framework of the average-atom model. Our results are compared to experimental data, as well as to other theoretical calculations, relying on the Ziman and Kubo-Greenwood formulations, and based on average-atom models or quantum-molecular-dynamics simulations. The impact of the definition of ionization, paying particular attention to the consistency between the definition and the perfect free electron gas assumption made in the formalism, is discussed. We propose a definition of the mean ionization generalizing to expanded plasmas the idea initially put forward for dense plasmas, consisting in dropping the contribution of quasibound states from the ionization due to continuum ones. It is shown that our recommendation for the calculation of the quasibound density of states provides the best agreement with measurements.

Systematic study of the stopping power of the lanthanides

In the last decade, lanthanides have become the subject of multiple studies due to their importance in technological applications. This paper aims to systematically study the energy loss per unit length of protons on the 15 lanthanides, from lanthanum to lutetium. We investigate the stopping power cross sections by considering the influence of the relativistic atomic structure, namely the description of the $4f$ electrons, the number of electrons in the valence shells, and the electronic screening of the same or close subshells. The electronic stopping model considers separate contributions from bound and valence electrons. We employ a many-electron model for the former and a combination of perturbative and nonperturbative free-electron gas approaches for the latter. Our stopping results for the lanthanide series cover an extended energy range from very low to the MeV region. We compare them with measurements and other theoretical (dpass, casp) and semiempirical (srim) methods. Our results agree with most experimental data, even the recent values around the maximum for gadolinium. We implement Lindhard's scaling for the stopping number for all the data available of the 15 targets. Lindhard scaling for the stopping number includes all the data for the 15 targets. The present paper cast doubts on certain data sets, which should affect srim's description of lanthanides, such as La, Nd, Dy, and Tb. We call attention to the scarcity of measurements in the low and intermediate ranges, and we suggest experimental efforts to shed light on the stopping power of these relevant targets.

Electronic Transport via Interstitial States in Mayenite Electride

Earlier theoretical calculations of the Seebeck coefficient of mayenite electride have shown that electrons are the major type of charge carriers, while experimental measurements show that the carriers are holes. We investigated the interplay between the experimentally observed deformation of Ca–Al–O cages in mayenite electride and its transport properties to reveal the reasons for this discrepancy. We found that the deformation of individual cages lifts the degeneracy of the electride subsystem and induces the localization of electrons in these interstices. This leads to significant changes in the band structure near the Fermi level, accompanied by splitting of the electride states into two subsystems separated by an indirect energy gap. As a result, the sign of the Seebeck coefficient changes and becomes positive, indicating that holes are the main type of charge carriers in accordance with the experimental observations. This outcome confirms that the mayenite electride subsystem cannot be considered as a homogeneous gas of free electrons but should be considered as partially localized electrons that can move through the crystal together with local deformations.

Electronic interaction of slow hydrogen, helium, nitrogen, and neon ions with silicon

We investigate the electronic excitation of silicon by hydrogen, helium, nitrogen, and neon ions for ion energies ranging from several tens to a few hundred kiloelectronvolts. Experiments are carried out in transmission geometry using a time-of-flight medium energy ion scattering system. The targets are self-supporting, single-crystalline Si (100) foils with nominal thicknesses of 50 and 200 nm. Stopping cross-sections (SCSs) are derived and compared with datasets available from the literature and predictions from theory. The results for H projectiles reveal good agreement with literature datasets, within quoted uncertainties. For He projectiles, the results show good agreement with most of the literature data. For N ions, higher values than reported in the literature are measured. For Ne, where literature data are scarce, we extend the velocity regime for which data exist by a factor of two toward higher velocities. The electronic SCS is found to be proportional to ion velocity for all impinging ions, for velocities below the Bohr velocity $(v&lt;{v}_{0})$. Comparison with theoretical predictions for a homogeneous free electron gas indicates strong contributions of local energy loss processes different from those expected for electron-hole pair excitation in binary collisions for all ions different from protons.