Fermi Gas Of Electrons Research Articles

Band Structures of Narrow Gap Semiconductors in Terms of Coulombic Polaron Effect

We consider the formation of a polaron in an interacting Fermi gas due to Coulomb polarization of electron gas by a single electron. We show that the polarization effect due to the Coulomb field in an interacting Fermi gas leads to the Coulomb polaron caused by the exchange-correlation hole and the electron spectrum shows an insulating behavior with the dispersion law of quasiparticles similar to the Kane kp-model of a band structure for narrow gap semiconductors. We apply the polaronic model to the case of inhomogeneous periodic and interacting electron Fermi gas of crystals. We show that the formation of the Coulomb polaron leads to the transition to the semiconductor with the energy bands similar to the well-known semiempirical Kane kp-model of the band structure of narrow gap semiconductors. We also discuss the impact of the results on band structure calculations.

Weibel instabilities in a completely degenerate electron Fermi gas

Weibel instability in a degenerate Fermi plasma is studied. A new type of quantum Weibel instabilities is disclosed. In particular, a novel oscillatory Weibel instability is found and its growth rate is obtained. A transverse zero sound in a quantum degenerate electron gas, which has no counterpart in the classical consideration, is revealed.

Electron acoustic soliton in a quantum magnetoplasma

A theoretical investigation is carried out for the first time to understand the linear and nonlinear properties of obliquely propagating electron-acoustic solitary waves (EASWs) in a two-electron population quantum magnetoplasma. A dispersion relation in the linear regime and the Zakharov–Kuznetsov (ZK) equation in the nonlinear regime are derived by using a quantum hydrodynamic set of equations. It is observed that the magnetic field contributes in the wave dispersion through the weakly transverse direction in the ZK equation. It is also found that propagation characteristics of the EASW are significantly affected by the presence of quantum corrections and the ratio of hot to cold electron concentration. The results presented in this study may be helpful to understand the salient features of the finite-amplitude localized electron acoustic solitary pulses in a two-population electron Fermi gas observed in laser-produced plasmas.

Electron propagation in crossed magnetic and electric fields

We analyse the dynamics of monoenergetic electrons in the presence of uniform, perpendicular magnetic and electric fields. The Green function technique is used to derive analytic results for the field-induced quantum mechanical drift motion of (i)?single electrons and (ii)?a dilute Fermi gas of electrons. The method yields the drift current and, at the same time it allows us to quantitatively establish the broadening of the (magnetic) Landau levels due to the electric field: level number k is split into k+1 sublevels that render the kth oscillator eigenstate in energy space. Adjacent Landau levels will overlap if the electric field exceeds a critical strength. Our analysis suggests an alternative mechanism of conductivity quantization in the quantum Hall effect. The results are of particular relevance in strong current configurations where the presence of a perpendicular electric field must be taken into account.

Ultrafast processes in Ag and Au: A Monte Carlo study

Monte Carlo simulations of ultrafast electron processes in Ag and Au have been used to analyze transient reflectivity as well as two-photon photoemission experiments. The model consisted of an electron Fermi gas coupled to longitudinal acoustic phonons. A laser pulse of finite width excited the electrons, after which the development of the distribution function was followed during 3‐5 ps. In the electron-phonon coupling we used the full q dependence of the scattering together with a semirealistic phonon dispersion relation. The strength of the electron-phonon scattering is governed by the deformation potential. Its value was fixed to low-fluence transient reflection data. Also hot-phonon effects were included. For the electron-electron scattering we employed a Coulomb interaction screened according to the Thomas-Fermi prescription. We accounted for exchange effects in the total scattering probability. In a later stage we varied the screening. We analyzed a variety of data for Ag and Au. A good description of the temperature dependence of the transient reflectivity for various excitation powers could be obtained. Also the time evolution of the Fermi surface showed fair agreement with the experiment. In the case of Ag the lifetime of an electron above the Fermi sea was predicted correctly. For Au, however, it was necessary to increase the screening to obtain the correct lifetimes of electrons excited above the Fermi sea. Using this adjusted screening the description of the other experiments no longer was appropriate. Finally also the resistivity due to electron-phonon scattering was predicted quite well using the deformation potential extracted from the ultrafast reflectivity experiments.

Strong bulk-edge coupling in the compressible half-filled quantum Hall state

We study bulk and edge correlations in the compressible half-filled state, using a modified version of the plasma analogy. The corresponding plasma has anomalously weak screening properties, and as a consequence we find that the correlations along the edge do not decay algebraically as in the Laughlin (incompressible) case, while the bulk correlations decay in the same way. The results suggest that due to the strong coupling between charged modes on the edge and the neutral fermions in the bulk, reflected by the weak screening in the plasma analogue, the (attractive) correlation hole is not well defined on the edge. Hence, the system there can be modeled as a free Fermi gas of electrons. We finally comment on a possible scenario, in which the Laughlin-like dynamical edge correlations may nevertheless be realized.

The Pauli Principle and the Restricted Primitive Model

The restricted primitive model is an electrically neutral, classical model consisting of hard spheres charged either +q or −q. We show that, by appropriately selecting the diameter of the hard spheres, the pressure when q=0 can be made equal to that for a fluid of Maxwell–Boltzmann point ions and an ideal Fermi gas of electrons. We compare the series expansion of these classical and quantum systems and find that, except for intermediate de Broglie density and moderate to strong electrical interaction strength, the restricted primitive model gives a reasonable representation of the pressure of the corresponding quantum system. Much of the current interest, however, has been focused on the above, excepted region.

Bifurcation of quantum nonlinear resonances induced by a time-periodic vector potential

The quantum mechanics of a two-dimensional ideal electron Fermi gas in a cylindrical cavity in the presence of a weak time-periodic vector potential is studied. Floquet eigenstates are obtained numerically and Husimi distribution functions are used to show the bifurcation and appearance of quantum nonlinear resonances. For electrons at the Fermi surface, if the frequency of the vector potential ${\mathrm{\ensuremath{\omega}}}_{0}$ is lower than a certain critical frequency ${\mathrm{\ensuremath{\omega}}}_{\mathrm{cr}}$ then there is no electron having a primary resonance. If ${\mathrm{\ensuremath{\omega}}}_{0}$ is higher than ${\mathrm{\ensuremath{\omega}}}_{\mathrm{cr}}$, electrons with certain angular momenta will have primary resonances.

Virial theorem and some properties of the electron gas in metals

The status of the virial theorem in classical and quantum mechanics is discussed and the principal virial relationships are derived. A model of the electron Fermi gas in a metal is considered taking explicit account of the consequences of the virial theorem for a stable system of electrons and ions interacting in accordance with the Coulomb law. This model is used to obtain expressions for the total energy and the chemical potential of the conduction electrons in undeformed and deformed metals. These expressions are used to estimate the equilibrium concentrations of electrons and ions, the electron work function of a metal, and the contribution of the collective-state electrons to the bulk modulus of a metal. It is shown that an electric field appears in an inhomogeneously deformed metal and that this field is proportional to the gradient of the bulk strains. A space charge, which is compensated by a surface charge of opposite sign, also appears in such a metal.

A degenerate electron gas model for solutions of aluminum in cryolite melts

It is shown that the measurements of Odegardet al.[1] of the solubility of Al at 1000 °C in alumina-saturated cryolite melts can be interpreted in terms of a degenerate Fermi gas of electrons in equilibrium with Na adsorbed on the Al interface. The effective mass of the electrons ism* = 0.085m°, wherem° is the rest mass of an isolated electron, and the bottom of the conduction band lies at 118 kJ (1.22 eV) below the level of electrons in pure sodium. These parameters also lead to a successful prediction of the observed depression of freezing point of NaF by Na, but only after deriving the appropriate relation to replace Raoult’s law. At NaF/AlF3 molar ratios ≤10., the treatment is inadequate; the observed solubilities are higher than predicted. This could be due to breakdown of the simplifying assumptions made or to the entry of a new factor, such as the occurrence of monovalent Al.

Influence of carrier lifetime on the cooling of a hot electron-hole plasma in GaAs

Abstract The influence of carrier lifetime on the cooling of a hot electron-hole plasma in bulk GaAs is studied by time-resolved photoluminescence. We observe a reduced cooling rate for samples with short carrier lifetime and an enhanced cooling rate for samples with long lifetime at high densities. The cooling rate is independent of carrier lifetime at low densities. The experimental data are in agreement with theory if the degeneracy of the electron and hole Fermi gas is taken into account.

Kinetic properties of two-dimensional metal systems

Abstract The two-dimensional degenerate Fermi gas of electrons interacting with phonons is considered. The basic mechanisms of momentum relaxation in such a system, associated with electron-phonon, phonon-phonon and electron-electron collisions, are shown to be qualitatively different from similar mechanisms in an ordinary three-dimensional metal. The physical explanation for this is that the two-dimensional system of interacting electrons and phonons breaks down into almost isolated groups, between which momentum transfer occurs through very slow, staged superdiffusion (mixing) processes. With certain structures of the Fermi surface, quasimomentum transfer through electron-electron collisions is insignificant; hence such collisions are not an efficient relaxation mechanism. In this paper an efficient method is suggested for deriving superdiffusion equations, based on the detailed-balance conditions in the electron-phonon system. A theory of low-temperature transport phenomena is developed for pure two-di...

Thermodynamic and electronic properties of alkali-metal atom fluids.

By use of a free-energy model, the properties of a fluid composed of neutral atoms and diatomic molecules, positive ions and molecular ions, and an electron Fermi gas are calculated. The interactions include excluded volume, internal molecular binding, electron-neutral s-wave scattering, and screened Hartree interactions. For rubidium and cesium parametrizations, the vapor-liquid phase transitions with their critical points, the insulator-metal transitions, and the isothermal electrical conductivities and magnetic susceptibilities are obtained.

Local-phonon model of strong electron-phonon interactions inA15compounds and other strong-coupling superconductors

We propose a model in which a single atom interacts strongly with a Fermi gas of spinless electrons. We find that the electrons provide an effective double-well potential for the atom. The electron-phonon coupling $\ensuremath{\Lambda}$ is renormalized downward with decreasing temperature, provided that $\ensuremath{\Lambda}$ is large at high temperatures. The model is consistent with the experimental temperature dependence of the Pauli susceptibility and the resistivity as well as with the violation of Mattheissen's rule. It provides a possible explanation for why the observed martensitic transition is so small. We find that the violation of Migdal's theorem implies time-retarded interactions between hops of the atom from one minimum of the double well to the other.

Quantum-Electrodynamic Corrections to the Electron Charge Value in Metals

The quantum-electrodynamic renormalization of the electron's charge when in a metal (Fermi gas of electrons) environment is calculated. Solid-state many-body techniques are employed rather than the usual quantum-electrodynamic approach, so that the analogy to calculating a material's dielectric constant is exhibited. In metals, the renormalized charge value is increased over the vacuum value by $\frac{\ensuremath{\delta}e}{e}\ensuremath{\cong}4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}\ensuremath{\rho}$, where $\ensuremath{\rho}$ is the metal's electron density in $\frac{e}{({10}^{\ensuremath{-}24}{\mathrm{cm}}^{3})}$. These corrections are too small to affect the recent measurements of $\frac{e}{h}$ in metals using the Josephson frequency-voltage relation for superconducting junctions, which are accurate to ${10}^{\ensuremath{-}6}$. Experiments to be done which will compare $\frac{e}{h}$ values in different metals to several orders of magnitude greater accuracy should detect the corrections to $e$ calculated in this paper.

Positron Annihilation in Metals

First-order perturbation theory has been applied to calculate the annihilation rate of positrons in a metal, represented by a Fermi gas of free electrons. In view of the possibility that a bound positronium atom may be formed, some justification is needed before perturbation theory may be used. Calculations on a simple model show that, owing to the presence of the many electrons in the Fermi gas and the operation of the Pauli exclusion principle, a perturbation expansion may indeed be employed in finding the electron density at the position of the positron. Another simple model is used to investigate the validity of calculating only up to the first order in the perturbation series. Higher orders are found to contribute a relatively small amount to the electron density provided the Fermi momentum is large. The condition is satisfied by aluminium, for which a lifetime of 2.8 × 10-10 sec is estimated.

Energy and Pressure of a Zero-Temperature Plasma.

The equation of state is considered for matter consisting of electrons and nuclei of atomic weight A and charge Z, at zero temperature and at densities much larger than that of the solid at zero pressure. Corrections are evaluated to the energy and pressure of a degenerate Fermi gas of noninteracting electrons, due to the following effectsn classical Coulomb energy of an ion lattice with uniformly distributed electrons (this is the largest correction); Thomas-Fermi deviations from uniform charge distribution of the electrons; and exehange energy and spin-spin interactions between the electrons. The corrections increase with decreasing density, and the approximations break down when the spacing between nuclei is greater than the mean radius of the free Thomas-Fermi atom, and the formulas are not applicable to the interior of planets. At very high densities, where the electrons are extremely relativistic, the correction to the pressure is a multiplying constant factor which is 0.994, 0.986, and 0.960, respectively, for Z = 2, 6, and 26. It is shown that the nuclei form a lattice rather than a gas. At very high densities, restrictions are found on possible values for A and Z due to inverse beta decays and pycnonuclear reactions. For instance,more » C/sup 12/ changes to Ne/sup 24/ at densities above 6 x 10/sup 9/ gm/cc. (auth).« less