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Physical review. B, Condensed matter

Phenomenological investigations ofS(k,ω) of the two-dimensional electron gas in the memory-function formalism

B. Tanatar

Published Jun 15, 1991• 3 citations

Abstract

The dynamic structure function S(k,\ensuremath{\omega}) and the dielectric function \ensuremath{\epsilon}(k,\ensuremath{\omega}) of the two-dimensional electron gas is calculated phenomenologically at ${\mathit{r}}_{\mathit{s}}$=1 and 5 in the memory-function formalism. The density-density response function \ensuremath{\chi}(k,\ensuremath{\omega}) is expressed in terms of that of a noninteracting system and an effective potential. The interaction part of the second-order memory function that determines the effective potential is approximated by a Gaussian in time domain. We use a consistent set of highly accurate ground-state static properties as input, coming from a Green's-function Monte Carlo calculation. The calculated S(k,\ensuremath{\omega}) shows a single-broad-peak structure at intermediate k, which is from the case in three dimensions.

DOI: 10.1103/physrevb.43.14621

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The dynamic structure function S(k,\ensuremath{\omega}) and the dielectric function \ensuremath{\epsilon}(k,\ensuremath{\omega}) of the two-dimensional electron gas is calculated phenomenologically at

{\mathit{r}}_{\mathit{s}}

=1 and 5 in the memory-function formalism. The density-density response function \ensuremath{\chi}(k,\ensuremath{\omega}) is expressed in terms of that of a noninteracting system and an effective potential. The interaction part of the second-order memory function that determines the effective potential is approximated by a Gaussian in time domain. We use a consistent set of highly accurate ground-state static properties as input, coming from a Green's-function Monte Carlo calculation. The calculated S(k,\ensuremath{\omega}) shows a single-broad-peak structure at intermediate k, which is from the case in three dimensions.

Variational and fixed-node Green's-function Monte Carlo calculations have been performed to find the ground-state properties of the two-dimensional electron gas in the density range 1\ensuremath{\le}

{r}_{s}

\ensuremath{\le}100. Our calculations predict a Wigner crystallization at the density

{r}_{s}

\ensuremath{\simeq}37\ifmmode\pm\else\textpm\fi{}5. The electron system is found to be in the normal- (paramagnetic) fluid state below the transition density, but the fully polarized state is very close in energy. We have tabulated the values of pair distribution function g(r), the static structure factor S(k), and the momentum distribution n(k) at several densities of interest both in the normal and the polarized phases. An estimate of the spin susceptibility \ensuremath{\chi} is also given.

We study the effects of disorder scattering on the ground-state energy of a two-dimensional electron system. Considering charged impurity scattering within the mode-coupling approximation to the memory function formalism, we calculate the correlation effects using a self-consistent field approach. In a different model, we also treat the disorder effects phenomenologically. The exchange, correlation, and ground-state energies and the compressibility are calculated for both models. In terms of the compressibility both models have similar predictions in the high-density region. The mode-coupling theory results at lower density are in better qualitative agreement with the experimental findings.

A new approach for the calculation of the linear response of both the ground and thermal-equilibrium states of many-electron systems is proposed via an integral formulation of the density-functional theory. Based on the path-integral representation of the one-particle Green's function, the frequency-dependent linear-response function for the Kohn-Sham noninteracting system is expressed as an explicit functional of the Kohn-Sham local potential, instead of the summation over the single-electron orbitals. Thus the dynamic linear density response can be determined as the solution of self-consistent equations which only need as input the total electron density of the ground or the equilibrium state. Exchange and correlation effects are incorporated. Because orbitals are not employed, the formulation provides the possibility for calculations of linear-response properties, such as dynamic polarizability and photoabsorption cross sections of systems with very many electrons. The present formulation can also be applied to general fermions.

We have evaluated the density-density response of the two-dimensional electron gas at zero temperature by solving the Dyson equation for the particle-hole Green's function, including exchange Coulomb matrix elements and short-range contributions in the ladder approximation. We study the effect of these correlations on the total energy, compressibility per particle, local field factor G ( q ), static structure factor and pair-correlation function. Results are compared with the normal random-phase approximation, local field theories and quantum Monte Carlo calculations.

We have used the variational and diffusion quantum Monte Carlo methods to calculate the energy, pair-correlation function, static structure factor, and momentum density of the ground state of the two-dimensional (2D) homogeneous electron gas. We have used highly accurate Slater-Jastrow-backflow trial wave functions and twist averaging to reduce finite-size effects where applicable. We compare our results with others in the literature and construct a local-density-approximation exchange-correlation functional for 2D systems.