Electron Momentum Distribution Function Research Articles

Nonexponential temperature dependence of the rate of threshold inelastic processes in dense media

The influence of the density of the medium on the temperature dependence of the rate constants of inelastic processes is investigated. It is shown that besides the effects like lowering of the ionization potential, which accelerate excitation and ionization processes in a nonideal plasma, there is a stronger mechanism for such acceleration, which is associated with the high frequency of collisions between particles and leads to destruction of the one-to-one relation between the energy and momentum of the particles in a dense medium. It is manifested by the presence of power-law tails in the equilibrium momentum distribution of the particles, which leads to a nonexponential temperature dependence of the rates of inelastic reactions in dense gases and nonideal plasmas. A kinetic equation for the generalized energy and momentum distribution function of electrons in an external electric field, which permits investigation of the effect under consideration under nonequilibrium conditions, is presented.

Electron acceleration and synchrotron radiation in decelerating plasmoids

An equation is derived to calculate the dynamics of relativistic magnetized plasma which decelerates by sweeping up matter from the ISM. Reduction to the non-radiative and radiative regimes is demonstrated for the general case of a collimated plasmoid whose area increases as a power of distance x from the explosion, and in the specific case of a blast-wave geometry where the area increases quadratically with x. An equation for the evolution of the electron momentum distribution function in the comoving fluid frame is used to calculate the observed synchrotron radiation spectrum. The central uncertainty involves the mechanism for transfering energy from the non-thermal protons to the electrons. The simplest prescription is to assume that a fixed fraction of the comoving proton power is instantaneously transformed into a power-law, “shock”-like electron distribution function. This permits an analytic solution for the case of a relativistic plasmoid with a constant internal magnetic field. Effects of parameter changes are presented. Breaks in the temporal behavior of the primary burst emission and long wavelength afterglows occur on two time scales for external ISM density distributions n ext α x − η . The first, as emphasized by Mészáros & Rees, represents the time when the outflow sweeps up ≈ M th/Γ 0 of material from the ISM, where M this the mass in the outflow ejecta and Γ 0 is the initial Lorentz factor of the plasmoid. The second represents the time when synchrotron cooling begins strongly to regulate the number of nonthermal electrons that are producing radiation which is observed at a given energy. Results are applied to GRB and blazar variability. The slopes of the time profiles of the X-ray and optical light curves of the afterglows of GRB 970228 and GRB 970508 are explained by injection of hard electron spectra with indices s < 2 in a deceleration regime near the radiative limit. We also propose that blazar flares are due to the transformation of the directed kinetic energy of the plasmoid when interacting with the external medium, as would occur if relativistic outflows pass through clouds orbiting the central supermassive black hole.

Ground-state properties and dynamics of the bilayer t-J model.

We present an exact diagonalization study of bilayer clusters of t-J model. Our results indicate a crossover between two markedly different regimes which occurs when the ratio J_perp/J between inter-layer and intra-layer exchange constants increases: for small J_perp/J the data suggest the development of 3D antiferromagnetic correlations without appreciable degradation of the intra-layer spin order and the d_(x2-y2) hole pairs within the planes persist. For larger values of J_perp/J local singlets along the inter-layer bonds dominate, leading to an almost complete suppression of the intra-layer spin correlation and the breaking of the intra-layer pairs. The ground state with two holes in this regime has s-like symmetry. The data suggest that the crossover may occur for values of J_perp/J as small as 0.2. We present data for static spin correlations, spin gap, and electron momentum distribution and spectral function of the `inter-layer RVB state' realized for large J_perp/J. The latter deviates from the single layer ground state, making it an implausible candidate for modelling high-temperature superconductors.

Slave-particle quantization and sum rules in the t-J model.

In the framework of constrained systems, we give the classical Hamiltonian formulation of slave-particle models and their correct quantization. The electron-momentum distribution function in the t-J and Hubbard models is then studied in the framework of slave-particle approaches and within the decoupling scheme. We show that criticisms that have been addressed in this context coming from a violation of the sum rule for the physical electron are not valid. Due to the correct quantization rules for the slave-particles, the sum rule for the physical electron is indeed obeyed, both exactly and within the decoupling scheme.

Spatial distribution of mobile holes in the t-J model.

We have calculated the hole-hole correlation function for two holes doped into a 5= 1/2 antiferromagnetic insulator described by the t Jmodel o-n a 16-site +8X ~32 lattice and a 24-site ~18X ~32 lattice using an exact diagonalization technique. We predict that the carriers described by this model, in the parameter range relevant to Cu02 planes, tend to stay as far apart as possible. This result is in direct contradiction to previously published exact diagonalization data [e.g., D. Poilblanc, Phys. Rev. B 49, 1477 (1994)].We suggest that if the carriers do tend to stay as far apart from one another as possible, then the electron momentum distribution function shows evidence for hole pockets at k=(~ m/2, ~ 7t/2), consistent with many recent studies of these models, including recent photoemission work.

Fermi surfaces and electronic topological transitions in metallic solid solutions

Notwithstanding the substitutional disorder, the Fermi surface of metallic alloys can be measured and computed. We show that, from the theoretical point of view, it is defined as the locus of the peaks of the Bloch Spectral Function (BSF). Such Fermi surfaces, on varying the atomic concentrations, may undergo changes of their topology, known as Electronic Topological Transitions (ETT). Thus, for instance, pockets of electrons or holes may appear or disappear, necks may open or close. ETTs cause anomalous behaviours of thermodynamic, transport and elastic properties of metals and constitute a fascinating field in the study of Fermi liquid systems. Although ETTs could be studied on pure systems as a function of the thermodynamic variables, nevertheless such a study would often require extreme conditions, and would lead to experimental difficulties. On the other hand, it is possible to explore the variations of atomic concentration, i.e. the valence electron per atom ratio, in metallic solid solutions with a relative experimental ease. In this paper we review the theoretical techniques for the determination of Fermi surfaces in metallic solid solutions and discuss some examples of ETTs, namely LiMg, ZrNb, NbMo, MoRe, AgPd, CdMg, NiW and NiTi alloys, also in connection with experimental data as thermoelectric power, resistivity, elastic constants and electron-phonon coupling and with the determinations of the electron momentum distribution function from Compton scattering and positron annihilation experiments. We show that the ab initio calculations of the electronic structure for the quoted systems, together with a careful determination of the BSF, are able to predict quantitatively ETTs at those concentrations where physical quantities display anomalies, so confirming directly ETT theory. Although it is not the purpose of the present review to give a full account of electronic structure calculation schemes, however, we briefly discuss the ideas and the main physical approximations underlying theories of substitutional disorder in alloys. We shall pay some more attention to the Coherent Potential Approximation (CPA) in the Korringa-Kohn-Rostoker (KKR) multiple scattering framework and the Hohenberg and Kohn Density Functional Theory in the Local Density Approximation (LDA) for the exchange-correlation potential. The above choice is supported by the numerical versatility of the LDAKKRCPA theory, and, more important, by the a fortiori evidence that essentially equivalent results are obtained from different theoretical frameworks, provided the same basic physical approximations are used. Accordingly, when convenient, we present new LDAKKRCPA determinations of the Fermi surfaces, as for the ZrNbMoRe series.

Slave-particle studies of the electron-momentum distribution in the low-dimensional t-J model.

The electron momentum distribution function in the $t-J$ model is studied in the framework of slave particle approach. Within the decoupling scheme used in the gauge field and related theories, we treat formally phase and amplitude fluctuations as well as constraints without further approximations. Our result indicates that the electron Fermi surface observed in the high-resolution angle-resolved photoemission and inverse photoemission experiments cannot be explained within this framework, and the sum rule for the physical electron is not obeyed. A correct scaling behavior of the electron momentum distribution function near $k \sim k_{F}$ and $k \sim 3k_{F}$ in one dimension can be reproduced by considering the nonlocal string fields [Z. Y. Weng et al., Phys. Rev. B45, 7850 (1992)], but the overall momentum distribution is still not correct, at least at the mean field level.

Electron-momentum distribution and spectral function for two holes in finite-cluster t-J models.

We calculated the momentum distribution and one-particle spectral function for the ground state of two holes in a finite-cluster t-J model in the framework of the string picture. Previous numerical results for these quantities could be reproduced at least qualitatively. Our interpretation of these data, however, supports a rigid-band approximation starting from the single-hole case rather than a nearest-neighbor hopping band and large Fermi surface. We argue that in order to interpret the finite-cluster data properly, it is crucial to take into account the well-established fact that the ground state of two holes in a finite cluster is a bound state with nontrivial symmetry.

Calculation of impact ionization coefficients with a third-order Legendre polynomial expansion of the distribution function

Values for impact ionization coefficients are calculated from the electron momentum distribution function. The distribution function is found by solving the Boltzmann transport equation. The solution is obtained by combining a third-order Legendre polynomial expansion with numerical methods which employ finite differences and sparse-matrix algebra. The calculated values for impact ionization agree with experiment and Monte Carlo simulations. Results obtained while using three versus two Legendre polynomials are compared. Calculations performed using three Legendre polynomials predict one half the impact ionization rate given by similar calculations using only two polynomials. Calculations predict that phonon scattering plays a much more significant role in carrier transport than does impact ionization.

Fokker-Planck code for the quasi-linear absorption of electron cyclotron waves in a tokamak plasma

We present the solution of the kinetic equation describing the quasi-linear evolution of the electron momentum distribution function under the influence of the electron cyclotron wave absorption, Coulomb collisions and the dc electric field in a tokamak plasma. The solution of the quasi-linear equation is obtained numerically using a two-dimensional initial value code following an ADI scheme. Most emphasis is given to the full non-linear and self-consistent problem, namely, the wave amplitude is evaluated at any instant and any point in space according to the actual damping. This is necessary since wave damping is a very sensitive function of the slope of the local momentum distribution function because the resonance condition relates the electron momentum to the location of wave energy deposition.

Hot-electron injection into the oxide in n-channel MOS devices

In recent years, interest in hot-electron injection current in MOS devices has increased due to advances in device concepts and technology. The injection current to the gate is the mechanism for programming FAMOS devices and determines the potential degradation of short-channel MOS devices due to electron trapping in the oxide. This work presents an accurate indirect current measurement technique based on charge transport to the floating gate in a FAMOS structure. The measurement bypasses effects of trapping and local heating, allowing full characterization of parameter, voltage, and temperature dependence down to gate current levels of 10-16A. Based on this characterization, a new qualitative model of hot-electron injection into the oxide is proposed. The basic assumption in the model is the spherical symmetry of the momentum distribution function of the hot electrons. This assumption leads to the experimentally observed dominant role of the lateral electric field in the pinchoff region in determining gate current behavior. The model provides an explanation of gate current parameter and voltage dependence, and suggests correlation between gate current and substrate impact ionization current in a range of operating voltages. This correlation is substantiated experimentally for a range of device parameters and voltages.

Relation of drift velocity to low-field mobility and high-field saturation velocity

From an investigation of the behavior of the momentum distribution function of electrons or holes under scattering rate and momentum scaling transformations, a number of interesting results are derived concerning the parameterization of drift-velocity–vs–electric-field relations in terms of mobility and saturation velocity. Indeed it is determined that saturation velocity is invariant under scaling of the magnitude of the scattering rates, which alters mobility, while mobility is invariant under scaling of the magnitude of the momentum, which alters saturation velocity. This independence between mobility and saturation velocity is utilized to generalize to interfaces velocity-field relations valid the the bulk. Using the transformation of drift velocity under both rate and momentum scaling, partial experimental data can be used to predict high-field saturation velocities. These velocities need not be reduced due to higher scattering rates as much as their low-field counterparts. Nonzero magnetic fields and nonuniform scaling are also considered.

Instability in one-dimensional systems

The electron-phonon interaction in one-dimensional electronic systems, in the half-filled tight binding form of the electron momentum distribution function, within the random-phase approximation, leads to instability of the systems, if the strength of the electron-phonon coupling constant exceeds π 2/8.

Non‐Linear Ultrasound Absorption in an Electromagnetic Wave Field under Quantum Size Effect Conditions

AbstractNon‐linear effects in dimensionally quantized films are considered at amplification of hypersound waves in an electromagnetic wave field with frequency Ω under the condition ql ≫ (q'quasimomentum of a phonon, l free‐path length of an electron). Strong resonance singularities in the sound absorption are observed under the condition qvov ∼ ω (v = 1, 2, 3, …, V0v Fermi velocity of the electron of the vth subband of the film, ω sound wave frequency). The momentum distribution function of electrons is distored. Under certain conditions the absorption is reversed to amplification.

Magnetic Scattering of X Rays from Electrons in Molecules and Solids

The scattering of moderately high-energy x rays from electrons in magnetic solids is analyzed. We show that (a) the incoherent Compton scattering of polarized x rays can be used to determine the spin-dependent momentum distribution function of electrons in ferromagnetic materials, and (b) the coherent Bragg scattering of unpolarized x rays can be used to determine the magnetic structure of antiferromagnetic solids below their transition temperature.

Extension of the Thomas-Fermi-Dirac Statistical Theory of the Atom to Finite Temperatures

The Thomas-Fermi theory of the atom is generalized to include the effects of temperature as well as exchange. This leads to a nonlinear integral equation for the Fermi electron-momentum distribution function, and the usual Poisson equation for the electron-density distribution. Analytical solutions of the integral equation are given for the limiting cases of near-degeneracy and complete nondegeneracy, and a numerical method of calculating solutions in the intermediate case is described. A complete discussion of the thermodynamics of the atom is given; in particular, it is shown that the Gibbs free energy is the product of the number of electrons and the electronic chemical potential (Fermi energy), despite statements which have been made to the contrary. Numerical results have verified the virial theorem for all $Z$, $T$, and atomic volumes. The ratio of the calculated energy for $T=\mathcal{P}=0$ to the experimental total ionization energy varies from 2.07 for H down to 1.33 for Al, and is presumably still closer to unity for higher-$Z$ elements. Some numerical results are given for iron over the density range 0.1 to 10 times normal and for values of $\mathrm{kT}$ from 0 to 1000 ev. Pressures, energies, and entropies are lower than the corresponding values calculated without exchange by as much as 40% at $kT=10$ ev, by up to 10% at $kT=100$ ev, and by only negligible amounts at $kT=1000$ ev.