Strong-field magnetotransport of conducting composites with a columnar microstructure

Abstract

The transport properties of composite conductors with a columnar microstructure, and subject to a strong uniform magnetic field perpendicular to the columnar axis, are discussed with special emphasis on the strong-field limit. Asymptotic considerations provide detailed insight into the factors that govern the local current distribution, and hence the bulk effective Ohmic resistivity components. Particularly explicit asymptotic results are found in the case of periodic arrays of long, parallel inclusions that are either perfect insulators or perfect conductors, and are embedded in a conducting host that is a simple, free-electron-like conductor. In some configurations, simple closed form expressions are derived for the current distribution as well as for the bulk effective resistivities. Numerical calculations of those distributions and resistivities are also performed and compared to the asymptotic expressions. We thus achieve a detailed understanding of the rich phenomenology of strong-field magnetotransport in such systems, some of which was predicted earlier from numerical calculations and subsequently found in a recent experiment.