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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We review some of the recent surprising theoretical and experimental results obtained on the transport properties of small disordered metal samples. Even in the presence of disorder, the quantum mechanical interference of electron wavefunctions can still be observed. The Aharonov-Bohm effect is a particularly clear demonstration of this. In doubly connected structures (such as loops of wire) threaded by a magnetic flux, the electrical conductance oscillates because of the Aharonov-Bohm effect. In fact, because the electron trajectories are diffusive (i.e. random walks), even a lone wire (a singly connected structure) will exhibit a random pattern of conductance fluctuations as a function of the magnetic field because of the same interference effects. All that is required for the observation of these interferences is that the electrons retain ‘phase memory’ duing the period of transit through the sample. The length over which memory is maintained (the phase coherence length) can be much larger tha...

Aharonov-Bohm effect in normal metal quantum coherence and transport

The transport through a segment of a disordered system is determined by the eigenvalues of a large random matrix. The effectively independent active transmission channels are associated with these eigenvalues which are closest to unity. A decreasing number of those survives when the system's length increases. They determine the conductance and its fluctuations, which are found to be independent, within broad limits, of the size, disorder and nature of the system. This universality is due to the strong correlations in the spectra of large random matrices, providing a new insight on and generalizing the extremely interesting recent results of Altschuler, Lee and Stone.

https://iopscience.iop.org/article/10.1209/0295-5075/1/5/008/pdf

Active Transmission Channels and Universal Conductance Fluctuations

Self‐consistent numerical solutions of the Poisson and Schrodinger equations have been obtained for the states of electrons under a narrow gate or under a narrow slit in a metal‐oxide‐silicon structure with an inner and an outer gate. For the cases considered (30‐nm‐wide gate and 80‐nm‐wide slit), the states of motion parallel to the Si‐SiO2 interface are more closely spaced than the states for motion perpendicular to the interface. It should be possible, for the structures considered, to achieve a dynamically one‐dimensional system with an electron density ≲106 cm−1.

R. F. Kwasnick

Papers

Nonmonotonic Variations of the Conductance with Electron Density in ∼70-nm-Wide Inversion Layers

Conductance fluctuations near the localized-to-extended transition in narrow Si metal-oxide-semiconductor field-effect transistors.