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

Abstract

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...

Ground-state energy and Wigner crystallization in thick two-dimensional electron systems

“…In our work, we do not repeat this calculation, but simply take the value of the parameter b, or other parameters needed to define the self-consistent solution for the subband. Moreover, as discussed below, such inhomogeneous densities can be replaced by a constant-density slab having an equivalent electrostatic potential, using the CDA discussed by Dharma-wardana [10]. The CDA method [10] involves replacing an inhomogeneous density η(z) by a slab of constant-density η of width a linked to η(z) by…”

“…Moreover, as discussed below, such inhomogeneous densities can be replaced by a constant-density slab having an equivalent electrostatic potential, using the CDA discussed by Dharma-wardana [10]. The CDA method [10] involves replacing an inhomogeneous density η(z) by a slab of constant-density η of width a linked to η(z) by…”

“…Here we have no QMC results for comparison. The total energy of the quasi-2D Wigner crystal is compared with the total en-ergy of the quasi-2D liquid [10]. Here the WT is found to occur at r s ∼15 to 21 in quasi-2D layers realized in clean HIGFETS,…”

“…However, although the 2D electrons reside in the (x, y)-plane, they have a transverse density η(z) confined to the lowest subband of the hetero-structure [1]. While the quasi-2D electron liquid has recently seen much attention, both experimental [11,12] and theoretical [10,13,14,15], the Wigner crystal in thick 2D layers has not been followed up since the work of Fujiki and Geldart [16]. Fujiki et al, have determined the effect of the 2D-layer thickness on the electrostatic energy and found that the hexagonal lattice is the most-stable crystal structure, as with the * Email: daniel.jost@ens-lyon.fr † Email for correspondence: chandre.dharma-wardana@nrc.ca δ-thin 2D layer (δ2D).…”

“…In this study we show that the single-Gaussian approximation, and the local-density approximation (LDA), can recover the QMC total energy with surprising accuracy. We also show that a method based on constructing a constant-density approximation (CDA) to the inhomogeneous density [10,20] can be profitably used for calculating the electrostatic potentials and the exchange-correlation energies of these systems.…”