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AIP conference proceedings

Dynamical correlation effects on pair-correlation functions of spin polarized two-dimensional electron gas

Krishan Kumar, Vinayak Garg, Rajinder Kumar Moudgil

Published Jan 1, 2013• 0 citations
Publisher

Abstract

We report a theoretical study on the spin-resolved pair-correlation functions gσσ′(r) of a two-dimensional electron gas having arbitrary spin polarization ζ by including the dynamics of exchange-correlations within the dynamical self-consistent mean-field theory of Hasegawa and Shimizu. The calculated g↑↑(r), g↓↓(r) and g↑↓(r) exhibit a nice agreement with the recent quantum Monte Carlo simulation data of Gori-Giorgi et al. However, the agreement for the minority spin correlation function g↓↓(r) decreases with increase in ζ and/or decrease in electron density. Nevertheless, the spin-summed correlation function remains close to the simulation data.

DOI
10.1063/1.4810544

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We report a theoretical study on the spin-resolved pair-correlation functions gσσ′(r) of a two-dimensional electron gas having arbitrary spin polarization ζ by including the dynamics of exchange-correlations within the dynamical self-consistent mean-field theory of Hasegawa and Shimizu. The calculated g↑↑(r), g↓↓(r) and g↑↓(r) exhibit a nice agreement with the recent quantum Monte Carlo simulation data of Gori-Giorgi et al. However, the agreement for the minority spin correlation function g↓↓(r) decreases with increase in ζ and/or decrease in electron density. Nevertheless, the spin-summed correlation function remains close to the simulation data.
We calculate the pair distribution function, g ( r ), in a two-dimensional electron gas and derive a simple analytical expression for its value at the origin as a function of r s . Our approach is based on solving the Schrödinger equation for the two-electron wavefunction in an appropriate effective potential, leading to results that are in good agreement with quantum Monte Carlo data and with the most recent numerical calculations of g (0) (Bulutay and Tanatar 2002 Phys. Rev. B 65 195116). We also show that the spin-up spin-down correlation function at the origin, , is mainly independent of the degree of spin polarization of the electronic system.
Based on its known exact properties and a new set of extensive fixed-node reptation quantum Monte Carlo simulations (both with and without backflow correlations, which in this case turn out to yield negligible improvements), we propose an analytical representation of (i) the spin-summed pair-distribution function and (ii) the spin-resolved potential energy of the ideal two-dimensional interacting electron gas for a wide range of electron densities and spin polarization, plus (iii) the spin-resolved pair-distribution function of the unpolarized gas. These formulas provide an accurate reference for quantities previously not available in analytic form, and may be relevant to semiconductor heterostructures and quantum dots both directly, in terms of phase diagram and spin susceptibility, and indirectly, as key ingredients for the construction of new two-dimensional spin density functionals, beyond the local approximation.
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.
Abstract In this paper, we theoretically investigate the effect of temperature on spin correlations in an unpolarized quasi-one-dimensional electron gas (Q1DEG). The correlations are treated dynamically within quantum version of the self-consistent mean-field approach of Singwi et al Numerical results for the ↑↑ and ↑↓ components of static structure factor and pair-correlation function, and the wave vector dependent static spin and charge susceptibilities are presented over a wide range of temperature T and electron coupling r s . We find that the recently reported (2020 J. Phys.: Condens. Matter. 32 335403) non-monotonic T -dependence of the contact pair-correlation function g ( r = 0; T ) is driven primarily by an interplay between ↑↓ correlations and thermal effects. At a given temperature, the dynamics of both ↑↑ and ↑↓ correlations is found to become significant with increasing coupling r s , manifesting unambiguously as pronounced peak at 3.5 k F (periodic oscillations) in the corresponding components of the structure factor (pair-correlation function). Analysis of static spin and charge susceptibilities reveals that an imbalance between ↑↑ and ↑↓ correlations may induce a transition to a spin-density wave (SDW) phase of wave vector ∼3.5 k F above a critical coupling for a sufficiently high T , while to a long-wavelength SDW phase at a low T . Higher the temperature, higher is the predicted critical coupling for the SDW phase. Interestingly, transition to the SDW phase is found to precede the recently predicted Wigner crystal instability in the finite- T Q1DEG. Further, if one starts with partially spin-polarized electrons, the SDW instability is found to shift to somewhat higher τ and r s . In addition, we have presented results for the free exchange-correlation energy, free correlation energy, and excess kinetic energy for the unpolarized and fully spin-polarized phases of the finite- T Q1DEG. Wherever interesting, we have compared our results with the predictions of the static version of the mean-field approach.
We have studied the spin-polarized three-dimensional homogeneous electron gas using the diffusion quantum Monte Carlo method, with trial wave functions including backflow and three-body correlations in the Jastrow factor, and we have used twist averaging to reduce finite-size effects. Calculations of the pair-correlation function, including the on-top pair density, as well as the structure factor and the total energy, are reported for systems of 118 electrons in the density range rs=0.5{r}_{\mathrm{s}}=0.5rs​=0.5--20 a.u., and for spin polarizations of 0, 0.34, 0.66, and 1. We consider the spin resolution of the pair-correlation function and structure factor, and the energy of spin polarization. We show that a control variate method can reduce the variance when twist averaging, and we have achieved higher accuracy and lower noise than earlier quantum Monte Carlo studies.
We construct a model for the value of the pair distribution function g ↑↓ (0) between antiparallel-spin electrons at contact in a two-dimensional electron gas with e 2 / r interactions, as a function of the coupling-strength parameter r s . The model involves an interpolation between the result of a low- r s expansion, including the second-order direct and exchange contributions to the energy in the paramagnetic state, and the result of a partial-wave phase-shift analysis near Wigner crystallization. The interpolation formula is in excellent agreement with many-body calculations based on the ladder approximation. We further show through an STLS self-consistent calculation that g ↑↓ (0) is essentially independent of the state of spin polarization of the electron gas.