Seminar on Disorder and strong electron correlations: "Modeling the two-dimensional electron gas in solid state devices"
( Università degli Studi di Trieste & INFM-CNR Democritos)
The electron gas (EG), a collection of point charges moving in a homogeneous neutralizing background, provides a far reaching paradigm underlying our current understanding of electronic systems. Nowadays, quasi two-dimensional electron gases of exceedingly high mobility are routinely available in the best laboratories around the world. This allows for the experimental investigation of the two-dimensional electron gas (2DEG) in the strong coupling regime, where the interplay between interaction and disorder scattering has unexpected effects, such as an apparent metal to insulator transition (MIT) which has attracted a considerable experimental and theoretical interest. Evidently, fine details of the devices hosting the quasi 2DEG play an important role in determining its properties and should be accounted for by theory. In actual solid-states realizations the 2DEG (i) has a finite transverse thickness, (ii) suffers scattering by a number of sources (scattering which in fact determines its mobility), and depending on the system (iii) occupies one or two valleys; moreover, (iv) in certain AlAs quantum wells it may have an in plane anisotropic kinetic energy (mass tensor). A property of the 2DEG that has recently received a lot of attention in connection with the MIT is the spin susceptibility χs. This measures the linear response of the electrons to an applied magnetic field that couples to the electron spin, causing a net spin polarization. We demonstrate that the EG model is perfectly capable of describing the available experimental evidence for χs once two conditions are met: relevant device details are included in the theoretical description and strong correlation effects are dealt with by a sufficiently accurate technique, such as quantum Monte Carlo simulations (QMC). In particular, we show that a perturbative account of disorder, based on the QMC predictions for the clean interacting 2DEG, yields for two-valley systems a divergence of χs with lowering the density in excellent agreement with the available experimental evidence for Si-MOSFETs.
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