Quantum-Wire Networks and the Quantized Hall Effect

Abstract

Networks of thin wires in a magnetic field (or without a magnetic field) are related to tight-binding models on the same nets. The Hall conductance of a two-dimensional regular or random network is quantized when the Fermi energy is in a gap of extended states. It provides the possibility that the novel quantized Hall effect in two-dimensional periodic systems predicted by Thouless et al. [Phys. Rev. Lett. 49 (1982) 405] is observed in an artificially constructed network.