Nonequilibrium Electron Distribution Function Research Articles

Effect of Nonequilibrium Transient Electronic Structures on Lattice Stability in Metals: Density Functional Theory Calculations

The electronic structures of metals undergo transient nonequilibrium states during the photoexcitation process caused by isochoric heating of X-ray free-electron laser, and their lattice stability is, thus, significantly affected. By going beyond frozen core approximation, we manually introduced nonequilibrium electron distribution function in finite-temperature density functional theory with the framework of Kohn–Sham–Mermin to investigate such transient states, and their effect on lattice stability in metals is demonstrated by phonon dispersion calculated using the finite displacement method. We found that the perfect lattice of a metal collapses due to the exotic electronic structure of nonequilibrium transient state created by isochoric heating of X-ray free-electron laser. Further increase of the number of holes created in the sample (i.e., an increase of laser fluence) still results in lattice instability for aluminum, while for copper, it results in phonon hardening. The potential energy surface is calculated for the extreme case of both Al and Cu with exactly one hole created in its inner shell for each one of the atoms. A double-well structure is clearly observed for Al, while the potential energy surface becomes steeper for Cu.

On relaxation processes in a completely ionized plasma

Relaxation of the electron energy and momentum densities is investigated in spatially uniform states of completely ionized plasma in the presence of small constant and spatially homogeneous external electric field. The plasma is considered in a generalized Lorentz model which contrary to standard one assumes that ions form an equilibrium system. Following to Lorentz it is neglected by electron-electron and ion-ion interactions. The investigation is based on linear kinetic equation obtained by us early from the Landau kinetic equation. Therefore long-range electron-ion Coulomb interaction is consequentially described. The research of the model is based on spectral theory of the collision integral operator. This operator is symmetric and positively defined one. Its eigenvectors are chosen in the form of symmetric irreducible tensors which describe kinetic modes of the system. The corresponding eigenvalues are relaxation coefficients and define the relaxation times of the system. It is established that scalar and vector eigenfunctions describe evolution of electron energy and momentum densities (vector and scalar system modes). By this way in the present paper exact close set of equations for the densities valid for all times is obtained. Further, it is assumed that their relaxation times are much more than relaxation times of all other modes. In this case there exists a characteristic time such that at corresponding larger times the evolution of the system is reduced described by asymptotic values of the densities. At the reduced description electron distribution function depends on time only through asymptotic densities and they satisfy a closed set of equations. In our previous paper this result was proved in the absence of an external electric field and exact nonequilibrium distribution function was found. Here it is proved that this reduced description takes also place for small homogeneous external electric field. This can be considered as a justification of the Bogolyubov idea of the functional hypothesis for the relaxation processes in the plasma. The proof is done in the first approximation of the perturbation theory in the field. However, its idea is true in all orders in the field. Electron mobility in the plasma, its conductivity and phenomenon of equilibrium temperature difference of electrons and ions are discussed in exact theory and approximately analyzed. With this end in view, following our previous paper, approximate solution of the spectral problem is discussed by the method of truncated expansion of the eigenfunctions in series of the Sonine polynomials. In one-polynomial approximation it is shown that nonequilibrium electron distribution function at the end of relaxation processes can be approximated by the Maxwell distribution function. This result is a justification of Lorentz–Landau assumption in their theory of nonequilibrium processes in plasma. The temperature and velocity relaxation coefficients were calculated by us early in one- and two-polynomial approximation.

Conductivity and Permittivity in Plasma With Nonequilibrium Electron Distribution Function

Electron conductivity and dielectric permittivity are essential parameters that determine the external characteristics of laboratory and space plasmas in terms of electromagnetic (EM) wave propagation. In most problems, $\sigma $ and $\varepsilon $ are calculated using the elementary theory under the assumption that the electron distribution function (EDF) is under equilibrium (Maxwellian). But, in real plasma, the EDF is, as a rule, non-Maxwellian. Therefore, the form of EDF can significantly affect the characteristics of various processes involving electrons. In this article, the calculations of the correction coefficients for conductivity and permittivity in argon were performed in a wide frequency range for typical two-temperature EDFs, with which almost any EDF in the laboratory and ionospheric plasma can be approximated. The results show that the form of EDF has a significant effect on the conductivity and the permittivity in plasma. Most substantial differences are observed under conditions when the frequency of the EM wave is less than the transport electron–gas collision frequency of electrons.

Nonlocal control of plasma conductivity

A study of the influence of the chemoionization processes on nonstationary gas-discharge conductivity has been performed. Due to energetic, suprathermal electrons, which appear in the chemoionization reactions, the highly nonequilibrium and time dependent nonlocal electron distribution function is formed. In such gas-discharge plasma, thermal electrons always have positive conductivity, while suprathermal, energetic electrons may have negative conductivity in heavy (argon, krypton, and xenon) noble gases dependent on conditions, which may lead to the nonmonotonic temporal behavior of gas-discharge plasma conductivity and potentially may create the absolute negative conductivity.

CURRENT DISTRIBUTION DEPENDENCE ON ELECTRIC FIELD IN HELICALLY COILED CARBON NANOTUBES

Experimentally is confirmed that helically coiled carbon nanotube (HCCNT) could be used as a small solenoid for generating spatially localized magnetic field. Current distribution during diffusive electronic transport likewise the inductivity of this quantum conductor depends on electric field. Despite slightly lower electron mobility in HCCNTs than that of the straight single wall carbon nanotubes, the coiled nanotubes are attractive for application as nonlinear nano-solenoids. Nonequilibrium electron distribution functions obtained by solving Boltzmann transport equation are used to predict average helical radius of current flow as a function of electric field intensity. Change of spatial distribution of electronic flow with applied electric field is considered and nonlinear inductivity of HCCNT is predicted.

Charge and energy fractionalization mechanism in one-dimensional channels

We study the problem of injecting single electrons into interacting one-dimensional quantum systems, a fundamental building block for electron quantum optics. It is well known that such injection leads to charge and energy fractionalization. We elucidate this concept by calculating the nonequilibrium electron distribution function in the momentum and energy domains after the injection of an energy-resolved electron. Our results shed light on how fractionalization occurs via the creation of particle-hole pairs by the injected electron. In particular, we focus on systems with a pair of counterpropagating channels, and we fully analyze the properties of each chiral fractional excitation which is created by the injection. We suggest possible routes to access their energy and momentum distribution functions in topological quantum Hall or quantum spin-Hall edge states.

CURRENT DISTRIBUTION DEPENDENCE ON ELECTRIC FIELD IN HELICALLY COILED CARBON NANOTUBES

Experimentally is confirmed that helically coiled carbon nanotube (HCCNT) could be used as a small solenoid for generating spatially localized magnetic field. Current distribution during diffusive electronic transport likewise the inductivity of this quantum conductor depends on electric field. Despite slightly lower electron mobility in HCCNTs than that of the straight single wall carbon nanotubes, the coiled nanotubes are attractive for application as nonlinear nano-solenoids. Nonequilibrium electron distribution functions obtained by solving Boltzmann transport equation are used to predict average helical radius of current flow as a function of electric field intensity. Change of spatial distribution of electronic flow with applied electric field is considered and nonlinear inductivity of HCCNT is predicted.

High-field electron transport in GaN under crossed electric and magnetic fields

High-field electron transport studied in crossed electric and magnetic fields in bulk GaN with doping of 1016 cm-3, compensation around 90% at the low lattice temperature (30 K). It was found the range of the magnetic and electric fields where the non-equilibrium electron distribution function has a complicated topological structure in the momentum space with a tendency to the formation of the inversion population. Field dependences of dissipative and Hall components of the drift velocity were calculated for the samples with short- and open- circuited Hall contacts in wide ranges of applied electric (0 — 20 kV/cm) and magnetic (1 — 10 T) fields. For former sample, field dependences of dissipative and Hall components of the drift velocity have a non-monotonic behavior. The dissipative component has the inflection point which corresponds to the maximum point of the Hall component. For latter sample, the drift velocity demonstrate a usual sub-linear growth without any critical points. We found that GaN samples with controlled resistance of the Hall circuit can be utilized as a electronic high-power switch.

A criterion of field reversal in a short glow discharge and its dependence on the parameters of the fluid model used

A criterion of field reversal in the near-cathode plasma of short glow discharge is considered. This criterion is shown to be extremely sensitive to the choice of the fluid-discharge model used (in particular, the choice of a Maxwellian or nonequilibrium electron-distribution function).

Electron–phonon relaxation and excited electron distribution in zinc oxide and anatase

We propose a first-principles method for evaluations of the time-dependent electron distribution function of excited electrons in the conduction band of semiconductors. The method takes into account the excitations of electrons by an external source and the relaxation to the bottom of the conduction band via electron–phonon coupling. The methods permit calculations of the non-equilibrium electron distribution function, the quasi-stationary distribution function with a steady-in-time source of light, the time of setting of the quasi-stationary distribution and the time of energy loss via relaxation to the bottom of the conduction band. The actual calculations have been performed for titanium dioxide in the anatase structure and zinc oxide in the wurtzite structure. We find that the quasi-stationary electron distribution function has a peak near the bottom of the conduction band and a tail whose maximum energy rises linearly with increasing energy of excitation. The calculations demonstrate that the relaxation of excited electrons and the setting of the quasi-stationary distribution occur within a time of no more than 500 fs for ZnO and 100 fs for anatase. We also discuss the applicability of the effective phonon model to energy-independent electron–phonon transition probability. We find that the model only reproduces the trends in the change of the characteristic times whereas the precision of such calculations is not high. The rate of energy transfer to phonons at the quasi-stationary electron distribution also have been evaluated and the effect of this transfer on the photocatalysis has been discussed. We found that for ZnO this rate is about five times less than in anatase.

Field-enhanced electron mobility by nonlinear phonon scattering of Dirac electrons in semiconducting graphene nanoribbons

The calculated electron mobility for a graphene nanoribbon as a function of applied electric field has been found to have a large threshold field for entering a nonlinear transport regime. This field depends on the lattice temperature, electron density, impurity scattering strength, nanoribbon width and correlation length for the line-edge roughness. An enhanced electron mobility beyond this threshold has been observed, which is related to the initially-heated electrons in high energy states with a larger group velocity. However, this mobility enhancement quickly reaches a maximum due to the Fermi velocity in graphene and the dramatically increased phonon scattering. Super-linear and sub-linear temperature dependence of mobility seen in the linear and nonlinear transport regimes. By analyzing the calculated non-equilibrium electron distribution function, this difference is attributed separately to the results of sweeping electrons from the right Fermi edge to the left one through the elastic scattering and moving electrons from low-energy states to high-energy ones through field-induced electron heating. The threshold field is pushed up by a decreased correlation length in the high field regime, and is further accompanied by a reduced magnitude in the mobility enhancement. This implies an anomalous high-field increase of the line-edge roughness scattering with decreasing correlation length due to the occupation of high-energy states by field-induced electron heating.

Charging of dust grains in a nonequilibrium plasma of a stratified glow discharge

A theoretical model is presented that describes the charging of dust grains in the positive plasma column of a stratified glow dc discharge in argon. A one-dimensional self-consistent model is used to obtain axial profiles of the electric field, as well as the electron energy distribution function along the axis of the discharge tube. Radial profiles of the electric field are determined in the ambipolar diffusion approximation. It is assumed that, in the radial direction, the electron distribution function depends only on the total electron energy. Two-dimensional distributions of the discharge plasma parameters are calculated and used to determine the potential and charge of a test dust grain at a certain point within the discharge and the electrostatic forces acting on it. It is shown that the grain charge distribution depends strongly on the nonequilibrium electron distribution function and on the nonuniform distribution of the electric field in a stratified glow discharge. A discussion is presented on the suspension of dust grains, the separation of grains by size in the discharge striations, and a possible mechanism for the onset of vortex dust motion at the edge of a dust cloud.

Nonlinear resistivity of a two-dimensional electron gas in a magnetic field

We develop a theory of nonlinear response to an electric field of a two-dimensional electron gas (2DEG) placed in a classically strong magnetic field. The latter leads to a nonlinear current-voltage characteristic at a relatively weak electric field. The origin of the nonlinearity is twofold: the formation of a nonequilibrium electron distribution function and the geometrical resonance in the inter-Landau-level transitions rates. We find the dependence of the current-voltage characteristics on the electron relaxation rates in the 2DEG.

Photon-assisted shot noise in mesoscopic conductors

We calculate the low-frequency current noise for AC biased mesoscopic chaotic cavities and diffusive wires. Contrary to what happens for the admittance, the frequency dispersion in noise is determined not by the electric response time (the “RC” time of the circuit), but by the time that electrons need to diffuse through the structure (dwell time or diffusion time). We find that the derivative of the photon-assisted shot noise with respect to the external AC frequency displays a maximum at the Thouless energy scale of the conductor. This dispersion comes from the slow, charge-neutral fluctuations of the non-equilibrium electron distribution function inside the structure. Our theoretical predictions can be verified with present experimental technology.

Frequency dispersion of photon-assisted shot noise in mesoscopic conductors

We calculate the low-frequency current noise for ac-biased mesoscopic chaotic cavities and diffusive wires. Contrary to what happens for the admittance, the frequency dispersion in noise is determined not by the electric response time (the RC time of the circuit), but by the time that electrons need to diffuse through the structure (dwell time or diffusion time). We find that the derivative of the photon-assisted shot noise with respect to the external ac frequency displays a maximum at the Thouless energy scale of the conductor. This dispersion comes from the slow, charge-neutral fluctuations of the nonequilibrium electron distribution function inside the structure. Our theoretical predictions can be verified with present experimental technology.

Investigation of various operation modes of a miniature superconducting detector of microwave radiation

Nonequilibrium electron and phonon distribution functions have been calculated for a metallic absorber of a promising miniature superconducting detector irradiated by microwave radiation. The response of this detector has been calculated, and it has been shown that this detector can operate in either the photon counter mode or bolometric mode in dependence on the degree of nonequilibrium of the phonon subsystem.

Microwave photoresponse in the two-dimensional electron system caused by intra-Landau-level transitions

The influence of microwave radiation on the DC-magnetoresistance of 2D-electrons is studied in the regime beyond the recently discovered zero resistance states when the cyclotron frequency exceeds the radiation frequency. Radiation below 30 GHz causes a strong suppression of the resistance over a wide magnetic field range, whereas higher frequencies produce a non-monotonic behavior in the damping of the Shubnikov-de Haas oscillations. These observations are explained by the creation of a non-equilibrium electron distribution function by microwave induced intra-Landau level transitions.

The efficiency of electron acceleration in solar type-IV radio pulsations with a zebra pattern

Based on a comprehensive analysis of the October 25, 1994 event, we consider the balance of energetic particles in a type-IV solar radio emission source with a zebra-type fine structure (in a coronal magnetic loop). The zebra pattern is formed through the injection of fast electrons into a trap and the formation of a ring-type nonequilibrium electron distribution function. We estimated the characteristic zebra-pattern lifetime, which is determined by the escape of fast particles from the trap into the loss cone. In addition, we determined the number of fast particles that must be injected into the trap to provide the observed radio brightness temperature in zebra-pattern stripes by analyzing the plasma emission mechanism responsible for the zebra-pattern generation. As a result, we estimated the efficiency of the electron acceleration mechanism in coronal magnetic loops at the post-flare evolutionary phase of an active region.

Thermionic phenomena in a nanoscale ring without carrier reservoirs: A thermionic couple

We have studied various thermionic processes in a small one-dimensional ring consisting of a metallic wire and an insulator which serves as the potential barrier for the charge carriers in the metallic wire. The ring is not connected to any particle reservoir, but at the two junctions it is attached to two phonon reservoirs with different temperatures. The lengths of both the metallic wire and the insulating part are shorter than the carrier mean free path, and therefore the nonequilibrium electron distribution function was solved using the Boltzmann-equation approach with electron-phonon interaction at the two junctions. We found that there is always a heat current flowing from the hot junction to the cold one. The electric current over the potential barrier increases monotonically as the Fermi energy in the metallic wire approaches the potential barrier height from below. Using a modulation doped semiconductor ring for numerical calculation, the thermionic current is found to be almost linear with respect to the temperature difference between the two junctions. Consequently, our system can be developed into a nanometer scale thermionic couple.

Effects of the electron energy distribution function on modeled x-ray spectra

This paper presents the results of a broad investigation into the effects of the electron energy distribution function on the predictions of nonlocal thermodynamic equilibrium collisional-radiative atomic kinetics models. The effects of non-Maxwellian and suprathermal ("hot") electron distributions on collisional rates (including three-body recombination) are studied. It is shown that most collisional rates are fairly insensitive to the functional form and the characteristic (central or average) energy of the electron distribution function as long as the characteristic energy is larger than the threshold energy for the collisional process. Collisional excitation and ionization rates are, however, highly sensitive to the number of hot electrons. This permits the development of robust spectroscopic diagnostics that can be used to characterize the electron density, bulk electron temperature, and hot electron fraction of plasmas with nonequilibrium electron distribution functions. Hot electrons are shown to increase and spread out plasma charge state distributions, amplify the intensities of emission lines fed by direct collisional excitation and radiative cascades, and alter the structure of satellite features in both K - and L -shell spectra. The characteristic energy, functional form, and spatial properties of hot electron distributions in plasmas are open to characterization through their effects on high-energy continuum and line emission and on the polarization of spectral lines.