Landolt-Börnstein - Group III Condensed Matter

12 Overview of the theory

Abstract

This chapter overviews the main results of the theory of quantum transport in quasi-one dimensional electron systems. The theory includes on i) quasi-1D ideal quantum wires, ii) impurity scattering and localization, iii) electrical transport and quantum transmission, iv) conductance fluctuations, v) persistent currents and vi) electron-electron interaction. The subject of quantum transport in almost ideal quasi-1D semiconductor systems has been treated exhaustively from both the experimental as well as the theoretical viewpoint. Ballistic transport is discussed including quantum point contacts, electron focusing and collimation as well as scattering in a junction of quantum wires and tunneling effects. The origin of the complete localization is that in one dimension an impurity can cause only forward and backward scattering, and that eventually with many impurities backward scattering dominates the states. As the DC-conductivity vanishes, alternatives of the conventional theories of electrical transport have to be explored in the quantum regime. Mainly, three approaches, (i) recursive Green function method, ii) linear response theory for conductance and quantum transmission, and iii) Thouless conjecture have been pursued. Since the DC-conductance at absolute zero depends exponentially on the length of a system, large statistical but reproducible fluctuations can be expected, when some parameter is changed for a given sample. The existence of persistent currents has been discussed for superconducting rings enclosing a magnetic flux and for normal metallic loops. Electron-electron scattering in low dimensions is a very important subject which has been pursued intensively during the past decades in connection with electrical transport.

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Title
12 Overview of the theory
Book Title
Electronic Transport. Part 1: Quantum Point Contacts and Quantum Wires
In
III Quantum Wires
Book DOI
10.1007/b55682
Chapter DOI
10.1007/10479560_71
Part of
Landolt-Börnstein - Group III Condensed Matter
Volume
34B1
Editors
  • B. Kramer
  • Authors
  • A. Fechner
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