Transport Effects on Signal Propagation in Quantum Wires

Currently, nanowire-based circuits are being considered as candidates for future high-speed electronics. Signal propagation in metallic carbon nanotubes has been analyzed using the Luttinger liquid theory to develop a transmission-line model showing features that can not be obtained from conventional transmission-line theory. The Luttinger liquid theory, however, is governed by strict conditions which restrict its application to metallic carbon nanotubes and it can not be used for any nanowire in general. In this paper, we present a unified theory that can be applied to wires ranging all the way from conventional three-dimensional conductors to one-dimensional carbon nanotubes. We show that when the number of current-carrying modes is less than a critical value, and the small-signal propagation characteristics are significantly influenced by transport effects which go beyond the conventional transmission-line theory. We also use our model to quantitatively examine a few potential applications.