Chaotic Transport in Antidot Lattices

Authors

Tsuneya Ando Department of Physics, Tokyo Institute of Technology

Publication Date

4/13/04

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Abstract

Advances in microfabrication and crystal growth technology have enabled the preparation of lateral superlattices with submicron structures on top of a two-dimensional (2-D) electron system with mean free path as large as 100 µm. The 2-D system modulated by a periodic strong repulsive potential is called antidot lattice. The transport in this system is ballistic (i.e., electrons are scattered from the antidot potential itself rather than from impurities). The purpose of this paper is to give a brief review on chaotic transport in antidot lattices in the presence of magnetic fields mainly from a theoretical point of view.

Various interesting phenomena have been observed in antidot lattices in magnetic fields: quenching of the Hall effect, Altshuler–Aronov–Spivak oscillation near vanishing fields, the so-called commensurability peaks in magnetoresistance, and fine oscillations around them.

Antidot lattices are introduced in “Antidot Lattices.” In “Commensurability Peaks,” the origin of commensurability peaks is discussed with emphasis on the roles of classical chaotic motion. In “Aharonov–Bohm-Type Oscillation,” the Aharonov–Bohm-type oscillation superimposed on the commensurability peak is analyzed based on semiclassical quantization of periodic orbits existing in the chaotic sea. Triangular lattices are discussed in “Triangular Antidot Lattices” with emphasis on differences from square lattices. In “Altshuler–Aronov–Spivak Oscillation,” a kind of the Altshuler–Aronov–Spivak oscillation appearing in weak magnetic fields is discussed in relation to the roles of inherent disorder in the antidot potential arising during the fabrication process. A new method based on a scattering matrix to calculate electronic states and transport properties is introduced in “Scattering Matrix Formalism,” together with some examples of the results obtained. A summary and conclusions are given in “Conclusion.”