Exchange and correlation energy of an inhomogeneous electron gas

A convenient expression is derived for the coefficient, B_xc(n), which determines the first gradient corrections to the exchange and correlation energy of an inhomogeneous electron gas. The result is exact to all orders in $\text{e}$² and is expressed in terms of the single particle progagator. A method of approximation, which is exact at high density, is given for the explicit evaluation of B_xc. Numerical results are given for B_xc in the metallic density range.     

Exchange and correlation in inhomogeneous electron systems

An exchange-correlation functional with a nonlocal density dependence is proposed. It fulfills a sum rule stating that the exchange-correlation hole should contain on electron, atom. We have used this functional as well as an earlier proposed approximation to calculate the exchange energy of atoms. The errors in the local density approximation are reduced by an order of magnitude, indicating that these improved functionals should be very useful for more complicated systems.     

Exchange and correlation effects in a semiconductor quantum-well wire

The exchange and correlation effects of a quasi-one-dimensional electron gas are investigated by using the self-consistent-field approximation theory proposed by Singwi, Tosi, Land and Sjölander for the response function of the electron system. The present results are applied to GaAs-GaAlAs rectangular quantum-well-wires with the appropriate form factors that take into account the influence of the finite width of the electron layer. The plasmon dispersion relation and structure factor are calculated as a function of electron density and thickness of the wire. Results for the total energy per electron including kinetic, exchange and correlation energies and electron effective mass are presented. The Hartree-Fock and the random-phase approximation (RPA) results are also presented for comparison. We have found that exchange and correlation effects are more evident in wires of reduced dimensions.     

Short-range correlation in electron gas

Short-range correlation between electrons with antiparallel spins is considered. Electron-electron ladder interactions are shown to be important for the short range correlation in the metallic and lower densities of electrons.     

Low-dimensional electron gas at semiconductor surfaces

In recent years, it has become possible to create well-ordered semiconductor surfaces with metallic surface states by using self-assembly of metal atoms. Since these states lie in the band gap of the semiconductor, they completely decouple from the substrate. In addition to two-dimensional structures it is possible to obtain arrays of one-dimensional atomic chains, which may be viewed as the ultimate nanowires. The dimensionality can be varied systematically by using vicinal surfaces with variable step spacing. Angle-resolved photoemission and scanning tunnelling spectroscopy reveal surprising features, such as a fractional band filling, nanoscale phase separation into doped and undoped chain segments, and a spin-splitting at a non-magnetic surface. Prospects for one-dimensional electron gas physics in atomic chains are discussed.     

The conductivity of the spin-polarized two-dimensional electron gas: Exchange/correlation and strong disorder effects

The conductivity of a spin-polarized two-dimensional electron gas is calculated and compared with the conductivity of the unpolarized electron gas. Disorder effects are considered within the self-consistent current relaxation theory, which gives rise to a crossover point from metallic to insulating behavior. Many-body effects due to exchange and correlation are taken into account and are described by a local-field correction. Our calculations are in good agreement with recent experimental results on the magnetoresistance of silicon inversion layers.     

Solitons in semiconductor microstructures with a two-dimensional electron gas

Nonlinear waves in a two-dimensional electronic plasma with metal screening gates are investigated. It is shown that solitons described by the KdV equation exist in such a system. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 7, 479–481 (10 October 1999)     

Ground state correlation in the two-dimensional polarized electron gas

The ground state energy and radial distribution functions of the polarized two-dimensional electron gas with valley degeneracyn _v =1 and 2 are calculated using the hypernetted-chain approximation with the effective correlation factor method for Fermions. The paramagnetic susceptibility is calculated and compared with experiment in silicon inversion layers.     

Alloy disorder scattering limited mobility of two-dimensional electron gas in the quaternary AlInGaN/GaN heterojunctions

Nitride heterojunction field effect transistors (HFETs) with quaternary AlInGaN barrier layers have achieved remarkable successes in recent years based on highly improved mobility of the two-dimensional electron gases (2DEGs) and greatly changed AlInGaN compositions. To investigate the influence of the AlInGaN composition on the 2DEG mobility, the quaternary alloy disorder (ADO) scattering to 2DEGs in AlInGaN/GaN heterojunctions is modeled using virtual crystal approximation. The calculated mobility as a function of AlInGaN alloy composition is shown to be a triangular-scarf-like curved surface for both cases of fixed thickness of AlInGaN layer and fixed 2DEG density. Though the two mobility surfaces are quite different in shape, both of them manifest the smooth transition of the strength of ADO scattering from quaternary AlInGaN to ternary AlGaN or AlInN. Some useful principles to estimate the mobility change with the Al(In,Ga)N composition in Al(In,Ga)N/GaN heterojunctions with a fixed 2DEG density are given. The comparison between some highest Hall mobility data reported for Al_xGa_1−xN/GaN heterojunctions (x=0.06~0.2) at very low temperature (0.3~13 K) and the calculated 2DEG mobility considering ADO scattering and interface roughness scattering verifies the influence of ADO scattering. Moreover, the room temperature Hall mobility data of Al(In,Ga)N/AlN/GaN heterojunctions with ADO scattering eliminated are summarized from literatures. The data show continuous dependence on Hall electron density but independence of the Al(In,Ga)N composition, which also supports our theoretical results. The feasibility of quaternary AlInGaN barrier layer in high conductivity nitride HFET structures is demonstrated.     

Note on the correlation energy of an electron gas

The residual ring diagram contribution which is due to the use of approximate eigenvalues and a momentum cutoff is evaluated and the terms of orderr _s in the correlation energy are given explicitly. The result is exact to orderr _s within neglect of the third order exchange contribution and improves the results of Du Bois, and Carr and Maradudin. The correlation energy plotted againstr _s connects rather smoothly to the low density results obtained recently by Stevens and Pokrant based on an entirely different variational method.This work was supported by the National Science Foundation     

The intrinsical character of the electronic correlation in an electron gas

By introducing the phase transformation of electron operators, we map the equation of motion of an one-particle Green's function into that of a non-interacting one-particle Green's function where the electrons are moving in a time-depending scalar potential and pure gauge fields for a D-dimensional electron gas, and we demonstrate that the electronic correlation strength strongly depends upon the excitation energy spectrum and collective excitation modes of electrons. It naturally explains that the electronic correlation strength is strong in the one dimension, while it is weak in the three dimensions.     

Short-range behavior of the pair correlation function in the dense electron gas

An effective Coulomb interaction taking into account the diffraction effects is used to sum the series of bubbles diagrams building up the short-range part of the pair correlation function.     

A self-consistent theory for exchange and correlation effects in electron gas

A theory of electron correlations giving self-consistently the compressibility and spin susceptibility is formulated within the generalized random-phase approximation.     

Spin polarization of two-dimensional electron gas in hybrid ferromagnetic/semiconductor nanostructures

We present a theoretical study on the spin-dependent transport of electrons in hybrid ferromagnetic/semiconductor nanosystem under an applied bias voltage. Experimentally, this kind of nanosystem can be realized by depositing a magnetized ferromagnetic stripe with arbitrary magnetization direction on the surface of a semiconductor heterostructure. It is shown that large spin-polarized current can be achieved in such a nanosystem. It is also shown that the spin polarity of the electron transport can be switched by adjusting the applied bias voltage. These interesting properties may provide an alternative scheme to realize spin injection into semiconductors, and such a nanosystem may be used as a tunable spin-filter by bias voltage.     

Exchange interaction and oscillations of the magnetization of the electron gas in a quantum cylinder

The exchange energy of the electron gas on a cylindrical surface in a constant magnetic field has been calculated. Analytical formulas describing the contribution of the exchange interaction into oscillations of the magnetization of the electron gas in a quantum cylinder have been obtained. It is shown that the magnetic response of the system exhibits Aharonov-Bohm oscillations for both degenerate and Boltzmann electron gases.