The metal insulator transition in two-dimensional systems with charged impurities

Gold, A.; Götze, W.

doi:10.1016/0038-1098(83)90765-2

Cited by 28 publications

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“…(2.31b), by disorder. This approximation, which replaces the interacting problem by an effective noninteracting problem, has been studied by Gotze (1983a, 1986) and has been used to analyze experiments Gotze, 1983b, 1985;Gold et al , 1984;Gold 1985aGold , 1985b.…”

Section: Disorder Renormalization Of Electron-electron and Electron-pmentioning

confidence: 98%

The Anderson-Mott transition

1994

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The interacting disordered electron problem is reviewed with emphasis on the quantum phase transitions that occur in a model system and on the field-theoretic methods used to describe them. An elementary discussion of conservation laws and diffusive dynamics is followed by a detai1ed derivation of the extended nonlinear sigma model, which serves as an effective field theory for the problem. A general scaling theory of metal-insulator and related transitions is developed, and explicit renormalization-group calculations for the various universality classes are reviewed and compared with experimental results. A discussion of pertinent physical ideas and phenomenological approaches to the metal-insulator transition not contained in the sigma-model approach is given, and phase-transition aspects of related problems, like disordered superconductors and the quantum Hall effect, are discussed. The review concludes with a list of open problems.

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Section: Disorder Renormalization Of Electron-electron and Electron-pmentioning

confidence: 98%

The Anderson-Mott transition

1994

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“…5 The static scattering rate a determines the mobility / LC = e/ma and the static conductivity cr = nefjt. e is the electron charge and m is the transport mass of the electron.…”

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Peak Mobility of Silicon Metal-Oxide-Semiconductor Systems

Gold

1985

Phys. Rev. Lett.

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The density dependence of the mobility of Si (100) inversion layers is calculated within a multiple-scattering theory. Two scattering mechanisms are included. Because of surface-roughness scattering and charged-impurity scattering, a peak mobility fx m is found at a characteristic electron density n m . The inclusion of a mobility edge for low electron densities sharpens the peak structure drastically in comparison with the linear scattering theory. The comparison of calculated mobilities with experimental results gives good agreement in the full measured density range.PACS numbers: 73.25.+ i, 73.40.Qv Mobility measurements in inversion layers are a widely used method to characterize the samples. 1 The reason for this is the specific electron-density dependence of the mobility. With increasing density n the mobility grows and reaches a maximum at a density of about some 10 12 cm" 2 and then decreases for higher density. The origin of the increasing mobility is the screening of the charged impurities, and the later decreasing mobility is due to increased surface-roughness scattering. 2 The peak mobility can characterize the sample. Systematic measurements, done by drifting Na + ions to the Si-Si0 2 interface, have shown 3 that the peak mobility is decreased with increasing density of the Na + impurities n t and that the peak position goes to higher n values.In the following, I give a new treatment of this effect by taking into account scattering by charged impurities and surface-roughness scattering within a nonlinear theory. The strongly peaked structure of the mobility-versus-density data is described by a mobility edge for low density. For high impurity densities the multiple-scattering effects influence the mobility for all electron densities. So for a quantitative description of the peak position a nonlinear theory is necessary. Good agreement of the density dependence of the mobility is reached within our frame for the first time.For the calculations of the mobility for temperature zero I use the self-consistent current-relaxation theory of Gotze 4 generalized to an interacting electron gas. 5 The static scattering rate a determines the mobility / LC = e/ma and the static conductivity cr = nefjt. e is the electron charge and m is the transport mass of the electron. Via a mode-coupling equation 5 a is given as(\U(q)\ 2 ) is the random potential, which is specified later. °(q,z) is the density relaxation function of the free-electron gas for wave vector q and complex fre-quency z = /a, given as °(q,z) = [Z°(q,z) -g°(q) ]/z. X°(q,z) is the two-dimensional Lindhard function, 6 g°(q) sss X 0 (q,z= s 0) 9 and for the local-field corrections I use the expression G(q) = q/2g v (q 2 -\-kf) l/2 . 7 g v is the valley degeneracy, V(q)F(q)is the effective electron-interaction potential given by V(q) = 27re 2 / (e L q), the Fourier transform of the Coulomb potential, and F(q) is a form factor due to the finite extent of the wave functions perpendicular to the surface [Eq.(2.52) of Ref. 1]. e L is the mean backgr...

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“…The authors of Refs. [27,[30][31][32][33] used their results without restrictions, although formally one should expect them to be valid only at r s 1. Below we show that our calculations yield a satisfactory agreement with the experiment even at r s ∼ 10.…”

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Spin polarization and exchange-correlation effects in transport properties of two-dimensional electron systems in silicon

2017

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We show that the parallel magnetic field-induced increase in the critical electron density for the Anderson transition in a strongly interacting two-dimensional electron system is caused by the effects of exchange and correlations. If the transition occurs when electron spins are only partially polarized, additional increase in the magnetic field is necessary to achieve the full spin polarization in the insulating state due to the exchange effects.PACS numbers: 71.10.-w, 71.27.+a, 71.30.+h The metal-insulator transition (MIT) in twodimensional (2D) electron systems, studied experimentally and theoretically in 1970s [1], was declared nonexistent after negative logarithmic quantum corrections to the conductivity had been found (for a review, see Ref.[2]). The reasoning was as follows. In an infinite 2D system, upon decreasing temperature, negative quantum logarithmic corrections to the conductivity will eventually become comparable to the conductivity itself. After this, conductivity will decrease exponentially. Therefore, the system will inevitably become an insulator no matter how high the initial value of the conductivity is. However, it has later been shown both theoretically [3][4][5][6] and experimentally [7,8] that this conclusion may be wrong in 2D systems with strong electron-electron interactions.Since there has been a certain amount of confusion and controversy in the literature regarding the zero-temperature MIT in infinite 2D systems (see, e.g., Ref.[9]), here we will consider a disorder-driven Anderson MIT at finite (although low) temperatures and in finite 2D systems. (As correctly stated in Ref. [10], the question about the true MIT is "a rather academic question as what has actually been measured experimentally corresponds to rather high energy physics".) Attempts to describe the experimentally observed behavior of the critical density for the MIT in silicon metaloxide-semiconductor field-effect transistors (MOSFETs) as a function of a parallel to the interface magnetic field, B, were made by quite a few theoretical groups [10][11][12][13][14][15]. Nevertheless, the satisfactory explanation of experimental results is still absent. Monte Carlo calculations and finite size scaling techniques [10,11] show that the spin polarization in strongly-correlated electron systems favors localization. Using the appraisal Ioffe-Regel criterion to calculate the critical density in the Born approximation with two fitting parameters, the authors of Ref. [12] have achieved a satisfactory agreement with the experiment, but correlation effects have not been taken into account and their negligibility in the case of strong electron-electron interactions has not been established. Doubts in the applicability of the percolation scenario to the transition in Si MOSFETs [13] are expressed in Ref. [12]. The increase of the effective mass with decreasing electron density suggests that the effect of interactions is the dominant driving force for the experimentally observed MIT due to fermion condensation [14] or the Wigner-...

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The metal insulator transition in two-dimensional systems with charged impurities

Cited by 28 publications

References 13 publications

The Anderson-Mott transition

The Anderson-Mott transition

Peak Mobility of Silicon Metal-Oxide-Semiconductor Systems

Spin polarization and exchange-correlation effects in transport properties of two-dimensional electron systems in silicon

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