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Physical review. B, Condensed matter

Spin-dependent analysis of two-dimensional electron liquids

Ceyhun Bulutay, B. Tanatar

Published May 2, 2002• 30 citations
Publisher

Abstract

Two-dimensional electron liquid (2D EL) at full Fermi degeneracy is revisited, giving special attention to the spin-polarization effects. First, we extend the recently proposed classical-map hypernetted-chain (CHNC) technique to the 2D EL, while preserving the simplicity of the original proposal. An efficient implementation of CHNC is given utilizing Lado's quadrature expressions for the isotropic Fourier transforms. Our results indicate that the paramagnetic phase stays to be the ground state until the Wigner crystallization density, even though the energy separation with the ferromagnetic and other partially polarized states become minute. We analyze compressibility and spin stiffness variations with respect to density and spin polarization, the latter being overlooked until now. Spin-dependent static structure factor and pair-distribution functions are computed; agreement with the available quantum Monte Carlo data persists even in the strong-coupling regime of the 2D EL.

DOI
10.1103/physrevb.65.195116

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Two-dimensional electron liquid (2D EL) at full Fermi degeneracy is revisited, giving special attention to the spin-polarization effects. First, we extend the recently proposed classical-map hypernetted-chain (CHNC) technique to the 2D EL, while preserving the simplicity of the original proposal. An efficient implementation of CHNC is given utilizing Lado's quadrature expressions for the isotropic Fourier transforms. Our results indicate that the paramagnetic phase stays to be the ground state until the Wigner crystallization density, even though the energy separation with the ferromagnetic and other partially polarized states become minute. We analyze compressibility and spin stiffness variations with respect to density and spin polarization, the latter being overlooked until now. Spin-dependent static structure factor and pair-distribution functions are computed; agreement with the available quantum Monte Carlo data persists even in the strong-coupling regime of the 2D EL.
Based on the mapping introduced by the classical-map hypernetted-chain (CHNC) method, classical numerical simulations, Monte Carlo and molecular dynamics, have been applied to the twodimensional electron fluid and the results are compared with those of quantum Monte Carlo simulations hitherto reported. It is shown that polarization properties of the ground state obtained by the diffusion Monte Carlo method are reproduced within the accuracy of quantum simulations by both of two mapping functions for the quantum temperature which have been proposed within the CHNC method. These results may serve as the basis of numerical simulations based on the CHNC method which are applicable to finite non-periodic systems like quantum dots and systems at finite temperatures.
We analyze the ground state of the two-dimensional quantum system of electrons confined in a parabolic potential with the system size around 100. We map the system onto a classical system on the basis of the classical-map hypernetted-chain (CHNC) method which has been proven to work in the integral-equation-based analyses of uniform unbounded systems and then apply classical numerical simulations. We find that the confined system undergoes the transition to the spin polarized state with the decrease of the average density and the corresponding critical value is as low as rs ∼ 0.3 in terms of the usual rs parameter estimated for the average density. As the ground state for given value of the rs parameter, our data give the critical value for the transition around 20 which is consistent with the known possibility. The advantage of our method is a direct applicability to geometrically complex systems which are difficult to analyze by integral equations. The application to the structure like quantum dots reported here is the first example of such applications.
We present a numerical calculation for the static spin-symmetric and spin-antisymmetric local-field factors as a function of density in a two-dimensional (2D) unpolarized electron liquid. We use a recent analytical expression for the spin-resolved pair distribution function of a 2D electron liquid based on quantum Monte Carlo simulation data and accurate correlation energy as input to construct the local-field factors from the fluctuation-dissipation theorem. We obtain good agreement with data from quantum Monte Carlo studies of the 2D electron liquid over an extensive range of density.
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}rs{r}_{s}rs​\ensuremath{\le}100. Our calculations predict a Wigner crystallization at the density rs{r}_{s}rs​\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.
A deeper understanding of low-dimensional and small-scale electronic systems requires an accurate characterization of the many-electron effects. Based on the electron liquid (EL) model, these many-body effects in the three-dimensional (3D) and two-dimensional (2D) electronic systems are dealt going beyond the random phase approximation within the zero-temperature framework. The dielectric formulation of the many-body problem is recapitulated and the longitudinal dielectric function of the EL is obtained using the self-consistent local-field correction scheme, known as STLS, under a general spin-valley degeneracy. Extensive explicit expressions are provided for the use of other researchers. The performance of this formalism is compared in both 3D and 2D by the quantum Monte Carlo data and the pseudopotential approach introduced by Pines and co-workers. STLS is observed to be a highly satisfactory technique, with some reservations on the long-wavelength behaviour. Ground-state energy, correlation energy and the isothermal compressibility of the 2D EL are computed using a variety of approaches. Negative compressibility and overscreening are discussed in the light of the recent experiments.
We present calculations of the energy, pair-correlation function (PCF), static structure factor (SSF), and momentum density (MD) for the one-dimensional electron gas using the quantum Monte Carlo method. We are able to resolve peaks in the SSF at even-integer multiples of the Fermi wave vector, which grow as the coupling is increased. Our MD results show an increase in the effective Fermi wave vector as the interaction strength is raised in the paramagnetic harmonic wire; this appears to be a result of the vanishing difference between the wave functions of the paramagnetic and ferromagnetic systems. We have extracted the Luttinger liquid exponent from our MDs by fitting to data around kF{k}_{\mathrm{F}}kF​, finding good agreement between the exponent of the ferromagnetic infinitely thin wire and the ferromagnetic harmonic wire.