De Palo<i>et al.</i>Reply:

Palo, S. De; Botti, M.; Moroni, Saverio; Senatore, G.

doi:10.1103/physrevlett.97.039702

Cited by 14 publications

(36 citation statements)

References 6 publications

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“…Such an interest encouraged us to extend our previous work on energies to the spin-resolved pair-distribution functions g σσ ′ (r, r ′ ) of the 2DEG, whose accuracy and availability in analytic form may serve a variety of purposes: the exchange-correlation hole and its dependence on the electron density and spin polarization may be relevant to the physics of the metal-insulator bifurcation in 2D 11 and to self-energy theories of the 2DEG, 12 but is * present address: Laboratoire de Chimie Théorique, Université Pierre et Marie Curie, Paris, France also needed for the estimate of the effects of the finite thickness on the spin susceptibility 13 and for the construction of generalized-gradient approximations (GGA) or weighted-density approximations (WDA) of density functionals, in analogy to the 3D case.…”

Section: 910mentioning

confidence: 99%

Pair-distribution functions of the two-dimensional electron gas

2004

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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 a new 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 formulae provide an accurate reference for quantities previously not available in analytic form, and may be relevant to semiconductor heterostructures, metal-insulator transitions 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.

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Section: 910mentioning

confidence: 99%

Pair-distribution functions of the two-dimensional electron gas

2004

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“…These g(r, ζ, w) can be calculated using the CHNC. On the other hand, the unperturbed-g approximation, found to be useful in Quantum Hall effect studies [8], has been exploited by De Palo et al [12]. They have used the pair functions g(r, ζ, w = 0) of the ideally thin layer obtained form QMC to calculate a correction energy ∆ given by, ∆E = (n/2) 2πrdr[W (r) − V (r)]h(r, ζ, w = 0) (26) Then the total exchange-correlation energy E xc (r s , ζ, w) is obtained by adding to ∆ the known E xc of the ideally- thin system.…”

Section: The Exchange-correlation Energy For Quasi-2d Layersmentioning

confidence: 99%

“…The long wavelength limit of the static response functions are connected with the compressibility or the spin-stiffness via the second derivative of the total energy with respect to the density or the spin polarization [25]. De Palo et al [12] have calculated m * g * from the QMC pair distribution functions and shown that they obtain quantitative agreement with the data for very narrow 2-D systems [41] as well as for the thicker systems found in HIGFETS [3]. The CHNC PDFs are close approximations to QMC results, and when used in Eq.…”

Section: The Spin-susceptibility Effective Mass and The G-factormentioning

confidence: 99%

Spin and temperature dependent study of exchange and correlation in thick two-dimensional electron layers

Dharma‐wardana

2005

Phys. Rev. B

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The exchange and correlation Exc of strongly correlated electrons in 2D layers of finite width are studied as a function of the density parameter rs, spin-polarization ζ and the temperature T . We explicitly treat strong-correlation effects via pair-distribution functions, and introduce an equivalent constant-density approximation (CDA) applicable to all the inhomogeneous densities encountered here. The width w defined via the CDA provides a length scale defining the z-extension of the quasi-2D layer resident in the x-y plane. The correlation energy Ec of the quasi-2D system is presented as an interpolation between a 1D gas of electron-rods (for w/rs > 1) coupled via a log(r) interaction, and a 3D Coulomb fluid closely approximated from the known three-dimensional correlation energy when w/rs is small. Results for the Exc(rs, ζ, T ), the transition to a spin-polarized phase, the effective mass m * , the Landé g-factor etc., are reported here.

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“…Although the z-motion is confined to the lowest subband, realistic layers may have widths of ∼ 600Å or more, and this corresponds to ∼ 6 effective atomic units in GaAs. Recent experiments and theory have focused on these layer-thickness effects [6,7,9,10,11]. The physics of such quasi-2DES depends on the density parameter r s , the layer thickness w which labels the z-charge distribution, the spin-polarization ζ, and the temperature T .…”

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confidence: 99%

“…The W (r) of the CDM is equivalent to that from the original inhomogeneous distribution, and only W (r) enters into the exchange-correlation and g(r) calculations. In the case of GaAs-HIGFETS, if the depletion density could be neglected [9], r s specifies the b parameter and hence the width w of the CDM. Then b 3 = 33/(2r 2 s ) and w = 2.09494r 2/3 s .…”

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confidence: 99%

Exchange-correlation and layer-thickness effects in quasi-two dimensional electron liquids

Dharma‐wardana¹

2005

Solid State Communications

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We use a mapping of the quasi-2D electron liquid to a classical fluid and use the hypernetted-chain equation inclusive of bridge corrections, i.e., CHNC, to calculate the electron pair-distribution functions and exchange-correlation energies as a function of the density, layer width, spin-polarization and temperature. The theory is free of adjustable parameters and is in good accord with recent effective-mass and spin-susceptibility results for HIGFET 2-D layers.PACS numbers: PACS Numbers: 05.30. Fk, 71.10.+x, 71.45.Gm The 2-D electron systems (2DES) present in GaAs or Si/SiO 2 nanostructures access a wide range of electron densities under controlled conditions, providing a wealth of information [1] which is of basic and technological importance. The 2DES is in the x-y plane and also has a transverse extension in the lowest sub-band of the hetero-structure [2]. The higher subbands are far above the Fermi energy and no upward excitations are possible. Although the z-motion is confined to the lowest subband, realistic layers may have widths of ∼ 600Å or more, and this corresponds to ∼ 6 effective atomic units in GaAs. Recent experiments and theory have focused on these layer-thickness effects [6,7,9,10,11]. The physics of such quasi-2DES depends on the density parameter r s , the layer thickness w which labels the z-charge distribution, the spin-polarization ζ, and the temperature T . The 2D density n defines the mean-disk radius r s = (πn)per electron, expressed in effective atomic units which depend on the bandstructure mass m b and the "background" dielectric constant ǫ b . Although r s is the "small parameter" in perturbation theory (PT), here it is simply the electron-disk radius and PT is not used.Finite-width effects of the 2DES arise also in the quantum Hall effect [4,5], where an "unperturbed-g" approximation, which uses the pair-distribution function (PDF) of the ideal 2DES and the quasi-Coulomb potential W (r) of the thick 2D layer are used to calculate energies.While diagrammatic methods propose "turn-key" procedures for calculating many-body properties, they work only for weakly coupled (small r s ) systems, where RPAlike approximations may be used. Varied results can be obtained using various approximations which go "beyond" RPA. Unfortunately, an approximation successful with one property usually fails for other properties. Such methods lead to negative PDFs, incorrect localfield corrections in the response functions, and disagreement with the compressibility sum rule etc., and incorrect predictions of spin-phase transitions (SPT) at quite high densities. In fact, alternative approaches were sought by Singwi, Tosi et al. (STLS)[12], and Ichimaru et al. [13], and also within the Feenberg-type correlatedwavefunction methods [14]. Most of the currently available results for strongly-coupled systems have been generated using correlated-wavefunction approaches via Quantum Monte Carlo (QMC) simulations. However, QMC remains a strongly computer-intensive numerical method which is best suited for the stu...

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De Paloet al.Reply:

Cited by 14 publications

References 6 publications

Pair-distribution functions of the two-dimensional electron gas

Pair-distribution functions of the two-dimensional electron gas

Spin and temperature dependent study of exchange and correlation in thick two-dimensional electron layers

Exchange-correlation and layer-thickness effects in quasi-two dimensional electron liquids

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