Spin susceptibility in a two-dimensional electron gas

Yarlagadda, Sudhakar; Giuliani, Gabriele F.

doi:10.1103/physrevb.40.5432

Cited by 44 publications

(30 citation statements)

References 35 publications

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“…Though not exact unless Ψ T has the same nodes as the unknown ground state, a condition not generally met, FN-QMC provides fairly accurate predictions for ground state properties of interacting fermion systems. Other approximate theories may fulfill such an accuracy requirement at weak coupling [19], but are not amenable to systematic improvement in the strongly correlated regime. When applied beyond their range of validity, they predict a variety of magnetic instabilities at unrealistically high densities [20].…”

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confidence: 99%

Spin-polarization transition in the two-dimensional electron gas

2001

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Abstract. -We present a numerical study of magnetic phases of the 2D electron gas near freezing. The calculations are performed by diffusion Monte Carlo in the fixed node approximation. At variance with the 3D case we find no evidence for the stability of a partially polarized phase. With plane wave nodes in the trial function, the polarization transition takes place at rs = 20, whereas the best available estimates locate Wigner crystallization around rs = 35. Using an improved nodal structure, featuring optimized backflow correlations, we confirm the existence of a stability range for the polarized phase, although somewhat shrunk, at densities achievable nowadays in 2 dimensional hole gases in semiconductor heterostructures . The spin susceptibility of the unpolarized phase at the magnetic transition is approximately 30 times the Pauli susceptibility.Quantum simulations show that the three-dimensional electron gas undergoes a continuous spin-polarization transition, upon decreasing the density into the strongly correlated regime, before forming a Wigner crystal [1,2]. Despite the theoretical interest of a simple model exhibiting quantum phase transitions [3], the difficulty of realizing a low density electron gas in real materials makes the contact with experiment a rather indirect one [4]. However, electrons can be confined into effectively two-dimensional systems, for instance in Si MOSFET's and III-V semiconductor heterostructures [5], over a density range extending down to the freezing transition [6].Far from being a mere playground for testing many-body theories and numerical simulations, strongly correlated two-dimensional electronic systems offer an extremely rich and interesting phenomenology, such as the fractional quantum Hall effect [7] and a previously unexpected metal-insulator transition [8], not to mention their relevance to superconductor cuprates [9]. Therefore, we think that it is useful to extend the work of ref.[2] and study the polarization transition of the two-dimensional electron gas (2DEG). In fact, spin fluctuations appears to play an important role in the 2DEG at the metal-insulator transition in presence of disorder [10]).c EDP Sciences

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confidence: 99%

Spin-polarization transition in the two-dimensional electron gas

2001

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“…By definition G + (q) is meant to represent the effects of the exchange and correlation hole surrounding each electron in the fluid and is therefore a key input in the density functional theory (DFT) of the inhomogeneous electron gas 1 and in studies of quasiparticle properties (such as the effective mass and the effective Landè g-factor) in the electronic Fermi liquid 2 . For what concerns DFT calculations, a common approximation to the unknown exchange-correlation energy functional E xc [n] appeals to its second functional derivative,…”

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confidence: 99%

Analytical expressions for the charge-charge local-field factor and the exchange-correlation kernel of a two-dimensional electron gas

et al. 2001

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We present an analytical expression for the static many-body local field factor G+(q) of a homogeneous two-dimensional electron gas, which reproduces Diffusion Monte Carlo data and embodies the exact asymptotic behaviors at both small and large wave number q. This allows us to also provide a closed-form expression for the exchange and correlation kernel Kxc(r), which represents a key input for density functional studies of inhomogeneous systems.PACS number: 71.10. Ca, 71.15.Mb The static charge-charge response function χ C (q) of a paramagnetic electron gas (EG) can be written in terms of the Lindhard function χ 0 (q) by means of the spin-symmetric many-body local field G + (q) through the relationshipThus G + (q) is a fundamental quantity for the determination of many properties of a general electron system. By definition G + (q) is meant to represent the effects of the exchange and correlation hole surrounding each electron in the fluid and is therefore a key input in the density functional theory (DFT) of the inhomogeneous electron gas 1 and in studies of quasiparticle properties (such as the effective mass and the effective Landè g-factor) in the electronic Fermi liquid 2 . For what concerns DFT calculations, a common approximation to the unknown exchange-correlation energy functional E xc [n] appeals to its second functional derivative,wheren is the average local density of the EG. The local field factor and the exchange-correlation kernel are simply related in Fourier transform bywhere d is the dimensionality of the system and v q is the Fourier transform of the Coulomb potential e 2 /r. In what follows we shall only consider the case of two spatial dimensions, with d = 2 and v q = 2πe 2 /q. The corresponding three-dimensional case was discussed in Ref. [3]. A number of exact asymptotic properties of the static local field factor in two dimensions are readily proven. In particular,withwhere k F = √ 2πn = √ 2/r s a B is the Fermi wave number, r s = πna 2 B is the usual EG density parameter with a B the Bohr radius, κ 0 = πr 4 s /2 is the compressibility of the ideal gas in units of a 2 B /Ryd, while κ is the compressibility of the interacting system. By making use of the thermodynamic definition of κ we can write1 where ǫ c (r s ) is the correlation energy per particle. Once this function is known, it is possible to calculate A + . For the present purpose ǫ c (r s ) can be taken from the Monte Carlo data of Ref. [4]. The asymptotic behavior of G + (q) at large q is also known exactly 5,6 :where C + is proportional to the difference in kinetic energy between the interacting and the ideal gas,Moreover B + = 1 − g(0), g(0) being the value of the pair-correlation function at the origin. For g(0) we use the simple expressionwhich has been derived 7 by 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. This interpolatio...

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“…It is known that the HF approximation, even for the density-response leads to unphysical instabilities which are removed at the level of RPA or higher order approximations. Divergence in the spin-response of a 2D electron gas was also found by Yarlagadda and Giuliani [37] in various approximations. More elaborate theories of spin correlations in 3D seem to indicate the existence of instability at a much lower density (i.e., high r s ) [14,38].…”

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confidence: 53%

Spin correlations in electron liquids: Analytical results for the local-field correction in two and three dimensions

Tanatar

Mutluay

1998

Eur. Phys. J. B

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Abstract. We study the spin correlations in two-and three-dimensional electron liquids within the sum-rule version of the self-consistent field approach of Singwi, Tosi, Land, and Sjölander. Analytic expressions for the spin-antisymmetric static structure factor and the corresponding local-field correction are obtained with density dependent coefficients. We calculate the spin-dependent pair-correlation functions, paramagnon dispersion, and static spin-response function within the present model, and discuss the spin-density wave instabilities in double-layer electron systems.PACS. 71.10.-w Theories and models of many electron systems -71.45.Gm Exchange, correlation, dielectric and magnetic functions, plasmons -73.20.Dx Electron states in low-dimensional structures (superlattices, quantum well structures and mutlilayers)

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Spin susceptibility in a two-dimensional electron gas

Cited by 44 publications

References 35 publications

Spin-polarization transition in the two-dimensional electron gas

Spin-polarization transition in the two-dimensional electron gas

Analytical expressions for the charge-charge local-field factor and the exchange-correlation kernel of a two-dimensional electron gas

Spin correlations in electron liquids: Analytical results for the local-field correction in two and three dimensions

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