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Journal of Physics A Mathematical and Theoretical

Effects of interactions in two dimensions

A. A. Shashkin, A. A. Kapustin, Eduard V. Deviatov, Valerii T. Dolgopolov, Zee Don Kvon, S. V. Kravchenko

Published May 8, 2009• 2 citations
Publisher

Abstract

Strong electron–electron interactions in dilute two-dimensional electron systems in silicon lead to Pauli spin susceptibility growing critically at low electron densities. This effect originates from renormalization of the effective mass rather than the g-factor. The relative mass enhancement is system and disorder independent, which suggests that it is determined by electron–electron interactions only.

DOI
10.1088/1751-8113/42/21/214010

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Strong electron–electron interactions in dilute two-dimensional electron systems in silicon lead to Pauli spin susceptibility growing critically at low electron densities. This effect originates from renormalization of the effective mass rather than the g-factor. The relative mass enhancement is system and disorder independent, which suggests that it is determined by electron–electron interactions only.
Electrons in two-dimensional (2D) layers at semiconductor interfaces may be driven to a solid phase by reducing their density. Understandmg of this electron liquid-solid transition at mK-temperatures and the origin of the 2D electron solid phase remain challenging. The experimental system under study is subject to strong interactions and disorder. Charge transport in the electron solid phase demonstrates many features anticipated for the pinned crystal, though no direct imaging of a spatial charge- or magnetic-ordering is available by now. Rich information has been recently obtained for dilute electron liquid phase on strong renormalization of the Pauli spin susceptibility, magnetization, and the effective mass. These data provide a set of the Fermi-liquid coupling parameters for densities down to and at the transition. The steep density dependence of the susceptibility is intriguing because it might indicate a developing magnetic transition, though it is more likely reflects a tendency to crystallization.
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.
This chapter focuses on experimental results obtained in low-disordered strongly interacting two-dimensional (2D) electron systems; in particular in (100)-silicon metal-oxide-semiconductor field-effect transistors (MOSFET). It describes the additional confirmation in favor of zero-temperature zero-field metal-insulator transition is provided by magnetic and thermopower measurements. The chapter argues that the metal-insulator transition in silicon samples with very low level of disorder is driven by interactions. In a low-disordered 2D electron system in silicon MOSFETs, the resistivity at a certain "critical" electron density shows virtually no temperature dependence over a wide range of temperatures. In 2000, it was experimentally found that the ratio between the spin and the cyclotron splittings in silicon MOSFETs strongly increases at low electron densities. The strong enhancement of the spin susceptibility has indicated that at low electron densities, the system behaves well beyond the weakly interacting Fermi liquid.
We determine the spin susceptibility $\ensuremath{\chi}$ in the weak interaction regime of a tunable, high quality, two-dimensional electron system in a GaAs∕AlGaAs\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{Ga}\mathrm{As}GaAs∕AlGaAs heterostructure. The band structure effects, modifying mass and ggg-factor, are carefully taken into accounts since they become appreciable for the large electron densities of the weak interaction regime. When properly normalized, $\ensuremath{\chi}$ decreases monotonically from 3 to 1.1 with increasing density over our experimental range from 0.1 to $4\ifmmode\times\else\texttimes\fi{}{10}^{11}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$. In the high density limit, $\ensuremath{\chi}$ tends correctly towards $\ensuremath{\chi}\ensuremath{\rightarrow}1$ and compare well with recent theory.