I. Introduction (Preface, Nanostructures in Si Inversion Layers, Nanostructures in GaAs-AlGaAs Heterostructures, Basic Properties). 
II. Diffusive and Quasi-Ballistic Transport (Classical Size Effects, Weak Localization, Conductance Fluctuations, Aharonov-Bohm Effect, Electron-Electron Interactions, Quantum Size Effects, Periodic Potential). 
III. Ballistic Transport (Conduction as a Transmission Problem, Quantum Point Contacts, Coherent Electron Focusing, Collimation, Junction Scattering, Tunneling). 
IV. Adiabatic Transport (Edge Channels and the Quantum Hall Effect, Selective Population and Detection of Edge Channels, Fractional Quantum Hall Effect, Aharonov-Bohm Effect in Strong Magnetic Fields, Magnetically Induced Band Structure).

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Quantum Transport in Semiconductor Nanostructures

Publisher Summary Quantum transport is conveniently studied in a two-dimensional electron gas (2DEG) because of the combination of a large Fermi wavelength and large mean free path. Semiconductor nanostructures are unique in offering the possibility of studying quantum transport in an artificial potential landscape. This is the regime of ballistic transport in which scattering with impurities are neglected. The chapter presents a self-contained account of these three novel transport regimes in semiconductor nanostructures. The study of quantum transport in semiconductor nanostructures is motivated by more than scientific interest. The fabrication of nanostructures relies on sophisticated crystal growth and lithographic techniques that exist because of the industrial effort toward the miniaturization of transistors. Conventional transistors operate in the regime of classical diffusive transport, which breaks down on short length scales. The discovery of novel transport regimes in semiconductor nanostructures provides options for the development of innovative future devices.

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Characteristics of level broadening and transverse conductivity of a two-dimensional electron system under extremely strong fields have been theoretically investigated in the simplest approximation without the difficulty of divergence, i e. in the so-called damping theoretical one. Those of various cases of short- and long-ranged scatterers have been obtained. To see the dependence on the range explicitly, numerical calculation has been performed for the system with scatterers with the Gaussian potential. Especially in case of short-ranged ones the peak value of the transverse conductivity has been shown to be $(N+1/2)e^{2}/\pi^{2}\hbar$ which depends only on the natural constants and the Landau level index. It has been argued from general point of view that this fact is approximately true without reference to kinds of approximations. Such characteristic of the conductivity was confirmed experimentally, but there still remain some problems as to the absolute value of the level width.

Theory of Quantum Transport in a Two-Dimensional Electron System under Magnetic Fields. I. Characteristics of Level Broadening and Transport under Strong Fields

The oscillatory enhancement of the g factor caused by the exchange interaction among electrons is calculated. The degree of the spin splitting of each Landau level observed in Schubnikov-de Haas oscillation is shown to be explained by the theory of the level broadening of Landau levels if such enhancement is taken into account. The g factor is also calculated under tilted magnetic fields, and the theoretical one is in excellent agreement with the experiment by Fang and Stiles, and with the similar one performed recently by Kobayashi and Komatsubara. It is proposed that the valley splitting is enhanced by just the same mechanism and that such enhancement is a possible reason why it is observed experimentally in low-lying Landau levels.

Theory of Oscillatory g Factor in an MOS Inversion Layer under Strong Magnetic Fields

Plasmons and magnetoplasmons in semiconductor heterostructures

Influence of a One-Dimensional Superlattice on a Two-Dimensional Electron Gas

We have measured the surface electron density and the magnetic field dependence of the extremes of the oscillatory quasiparticle $g$ factor in a two-dimensional electron gas.

Experimental Study of Oscillatory Values of g * of a Two-Dimensional Electron Gas

Thermoelectric power of TiSe 2-x S x mixed crystals at low temperatures

We report the observation of Shubnikov-de Haas oscillations in the conductivity of surface holes in a $p$-type inversion layer of Si. The hole plasma is shown to be two dimensional. The effective mass varies from about $0.6{m}_{0}$ to $1{m}_{0}$ in the carrier concentration range (1 to 3.5) \ifmmode\times\else\texttimes\fi{} ${10}^{12}$ ${\mathrm{cm}}^{\ensuremath{-}2}$. It is proposed that the nonparabolic nature of Si valence band as well as many-body interaction affects the value of the effective mass. The hole gas is found to exist in one valley. Unexpected oscillations in the conductivity at low carrier concentration (less than 8 \ifmmode\times\else\texttimes\fi{} ${10}^{11}$ ${\mathrm{cm}}^{\ensuremath{-}2}$) are reported.

Oscillatory Magnetoconductance of p-Type Inversion Layers in Si Surfaces

Evidence is presented for periodic structure at the Si–SiOx interface in MOSFET’s in which the interface is a vicinal plane of (100). The results are discussed in terms of their relevance to interface technology.

Amir A. Lakhani

Papers

Influence of a One-Dimensional Superlattice on a Two-Dimensional Electron Gas

Experimental Study of Oscillatory Values of g * of a Two-Dimensional Electron Gas

Thermoelectric power of TiSe 2-x S x mixed crystals at low temperatures

Oscillatory Magnetoconductance of p-Type Inversion Layers in Si Surfaces

Evidence for a superlattice at Si–SiOx interface