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Physical review. B, Condensed matter

Effects of disorder on the ground-state energy of a two-dimensional electron gas

Reza Asgari, B. Tanatar

Published Feb 4, 2002• 9 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.65.085311

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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.
Starting from the quantum Monte Carlo (QMC) prediction for the ground-state energy of a clean two-dimensional one-valley (2D1V) electron gas, we estimate the energy correction due to scattering sources present in actual devices such as AlAs quantum wells and GaAs heterostructures. We find that the effect of uncorrelated disorder, in the lowest (second) order in perturbation theory, is to enhance the spin susceptibility leading to its eventual divergence. In the density region where the Born approximation is able to reproduce the experimental mobility, the prediction for the spin susceptibility yielded by perturbation theory is in very good agreement with the available experimental evidence.
We discuss interaction effects for the one-dimensional electron gas with a repulsive \ensuremath{\delta}-function interaction potential by using the random-phase approximation and a local-field correction. Analytical results for the local-field correction of charge-density fluctuations and spin-density fluctuations are obtained. The ground-state energy is found to be in better agreement with the exact result than the ground-state energy calculated within the random-phase approximation. We calculate the pair-correlation functions for electrons with parallel and antiparallel spins and the paramagnetic susceptibility. The energies of the collective density modes ${\mathrm{\ensuremath{\omega}}}_{\mathrm{d}}$ (q) and the collective spin modes ${\mathrm{\ensuremath{\omega}}}_{\mathrm{s}}$ (q) are calculated and compared with the energy of the electron-hole excitations ${\mathrm{\ensuremath{\omega}}}_{\mathrm{eh}\ifmmode\pm\else\textpm\fi{}}$ (q): ${\mathrm{\ensuremath{\omega}}}_{\mathrm{d}}$ (q\ensuremath{\rightarrow}0)>${\mathrm{\ensuremath{\omega}}}_{\mathrm{eh}\ifmmode\pm\else\textpm\fi{}}$ (q\ensuremath{\rightarrow}0)>${\mathrm{\ensuremath{\omega}}}_{\mathrm{s}}$ (q\ensuremath{\rightarrow}0). The critical exponents for the long-distance behavior of correlation functions are found to be described by local-field corrections. We compare our results for the critical exponents with recent results obtained by bosonization techniques and the conformal field theory.
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 rs{\mathit{r}}_{\mathit{s}}rs​=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.
The ground state of a two-dimensional charged-boson system is investigated over the range of densities 1\ensuremath{\lesssim}Rs{R}_{s}Rs​\ensuremath{\lesssim}10 in the self-consistent-field approximation; Rs{R}_{s}Rs​=(a02{a}_{0}^{2}a02​\ensuremath{\pi}\ensuremath{\rho}${)}^{\mathrm{\ensuremath{-}}1/2}$, where a0{a}_{0}a0​ is the Bohr radius and \ensuremath{\rho} is the number density. Starting with numerical self-consistent calculations of the static structure factor, the elementary excitation, pair-correlation functions, pressure, and ground-state energy are evaluated. These results are compared with those of the two-dimensional and three-dimensional systems obtained from other methods. The ground-state energy is given as ${\mathit{E}}_{0=\mathrm{\ensuremath{-}}1.2918{\mathit{R}}_{\mathit{s}}}^{\mathrm{\ensuremath{-}}2/3}$+0.03, which improves that result from the ring-diagram approximation.
We calculate the ground-state energy and the effective spin Land\'e g factor (g∗{\mathit{g}}^{\mathrm{*}}g∗) of a two-dimensional electron gas in strong magnetic fields using a variational Monte Carlo method and many-body trial wave functions composed of the Jastrow correlation factor and the Laughlin-type functions. We find that g∗{\mathit{g}}^{\mathrm{*}}g∗ increases with decreasing of electron density and also shows increasing behavior as the filling factor \ensuremath{\nu} decreases in the region of 12. At \ensuremath{\nu}=1.0, g∗{\mathit{g}}^{\mathrm{*}}g∗ is estimated to be about 11 for a dimensionless parameter rs{\mathit{r}}_{\mathit{s}}rs​=1.33, as compared to the measured value of 7.3, while considering impurity and phonon scatterings gives a better agreement of g∗{\mathit{g}}^{\mathrm{*}}g∗=9. \textcopyright{} 1996 The American Physical Society.
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.