Quantum Wires and Devices

Abstract

The mathematical physics of quantum wires has developed over the last two decades. In this volume the focus will be on precise results which have been discovered regarding resonance and bound states that appear in quantum wires, Anderson localization in quantum devices, the quantum Hall effect, and graphical models of quantum wire systems. Nanotechnology today permits the fabrication of semiconductors of a variety of shapes. Using a high mobility material like Al _x Ga _1-x As/GaAs, there is a quasi two dimensional electron gas (2DEG) residing at the interface of the heterojunction. By means of a split gate deposited on the heterojunction surface, the electron gas may be confined into a quasi-one dimensional channel. The gate can be lithographically designed to shape the electron gas into other mesoscopic structures such as intersecting wires, curved wires, rings, dots, stadia and so on. In these devices, quantum mechanical effects become apparent especially at low temperatures where the electron mean free path can be quite large.