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arXiv:0905.2706 · Journal of Physics A Mathematical and Theoretical

Disorder effect on the spin susceptibility of the two-dimensional one-valley electron gas

S. De Palo, Saverio Moroni, Gaetano Senatore

Published May 8, 2009• 2 citations
arXivHTMLPDF

Abstract

Starting from the quantum Monte Carlo (QMC) prediction for the ground-state energy of a clean two-dimensional one-valley (2D1V) electron gas, we estimate the energy correction due to scattering sources present in actual devices such as AlAs quantum wells and GaAs heterostructures. We find that the effect of uncorrelated disorder, in the lowest (second) order in perturbation theory, is to enhance the spin susceptibility leading to its eventual divergence. In the density region where the Born approximation is able to reproduce the experimental mobility, the prediction for the spin susceptibility yielded by perturbation theory is in very good agreement with the available experimental evidence.

DOI
10.1088/1751-8113/42/21/214013

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Starting from the quantum Monte Carlo (QMC) prediction for the ground-state energy of a clean two-dimensional one-valley (2D1V) electron gas, we estimate the energy correction due to scattering sources present in actual devices such as AlAs quantum wells and GaAs heterostructures. We find that the effect of uncorrelated disorder, in the lowest (second) order in perturbation theory, is to enhance the spin susceptibility leading to its eventual divergence. In the density region where the Born approximation is able to reproduce the experimental mobility, the prediction for the spin susceptibility yielded by perturbation theory is in very good agreement with the available experimental evidence.
We report measurements of the spin susceptibility in dilute two-dimensional electrons confined to a 45 A wide AlAs quantum well. The electrons in this well occupy an out-of-plane conduction-band valley, rendering a system similar to two-dimensional electrons in Si-MOSFETs but with only one valley occupied. We observe an enhancement of the spin susceptibility over the band value that increases as the density is decreased, following closely the prediction of quantum Monte Carlo calculations and continuing at finite values through the metal-insulator transition.
We find that the spin susceptibility of a two-dimensional electron system with valley degeneracy does not grow critically at low densities, at variance with experimental results [A. Shashkin et al., Phys. Rev. Lett. 96, 036403 (2006)]. We ascribe this apparent discrepancy to the weak disorder present in experimental samples. Our prediction is obtained from accurate correlation energies computed with state of-the-art diffusion Monte Carlo simulations and fitted with an analytical expression which also provides a local spin density functional for the system under investigation.
We find that the spin susceptibility of a two-dimensional electron system with valley degeneracy does not grow critically at low densities, at variance with experimental results [A. Shashkin et al., Phys. Rev. Lett. 96, 036403 (2006)]. We ascribe this apparent discrepancy to the weak disorder present in experimental samples. Our prediction is obtained from accurate correlation energies computed with state-of-the-art diffusion Monte Carlo simulations and fitted with an analytical expression which also provides a local spin density functional for the system under investigation.
The properties of a two-dimensional electron gas (2DEG) in a semiconductor host with two valleys related by an underlying C4{C}_{4}C4​ rotational symmetry are studied using Hartree-Fock and various other many-body approaches. A familiar artifact of the HF approach is a degeneracy between the valley-polarized---``Ising nematic''---and spin-polarized---ferromagnetic---phases, which is inconsistent with recent variational Monte Carlo (VMC) results. Correlation effects, computed either within the random phase approximation (RPA) or the T-matrix approximation, enhance the valley susceptibility relative to the spin susceptibility. Extrapolating the results to finite interaction strength, we find a direct first-order transition from a symmetry-unbroken state to a spin-unpolarized Ising nematic fluid with full valley polarization, in qualitative agreement with VMC. The RPA results are also reminiscent of experiments on the corresponding 2DEG in AlAs heterostructures.
We study the effects of disorder scattering on the ground-state energy of a two-dimensional electron system. Considering charged impurity scattering within the mode-coupling approximation to the memory function formalism, we calculate the correlation effects using a self-consistent field approach. In a different model, we also treat the disorder effects phenomenologically. The exchange, correlation, and ground-state energies and the compressibility are calculated for both models. In terms of the compressibility both models have similar predictions in the high-density region. The mode-coupling theory results at lower density are in better qualitative agreement with the experimental findings.
We report measurements of the spin susceptibility in dilute (rs{r}_{s}rs​ up to $\ensuremath{\approx}10$) AlAs two-dimensional (2D) electrons occupying a single conduction-band valley with an anisotropic in-plane Fermi contour, characterized by longitudinal and transverse effective masses ml{m}_{l}ml​ and mt{m}_{t}mt​. As the density is decreased, the spin susceptibility is significantly enhanced over its band value, reflecting the role of interaction. Yet the enhancement is suppressed compared to the results of quantum Monte Carlo based calculations that take the finite thickness of the electron layer into account but assume an isotropic effective mass equal to ml.mt\sqrt{{m}_{l}.{m}_{t}}ml​.mt​​. Proper treatment of an interacting 2D system with an anisotropic effective mass therefore remains a theoretical challenge.