Several properties of the Landauer resistance of finite repeated structures are derived. A theorem relating the energies of unity transmission through a finite repeated structure to the band structure of an infinite superlattice formed by periodic repetition of the finite structure [Vezzetti and Cahay, J. Phys. D 19, L53 (1986)] is generalized to the case of structures with spatially varying effective mass. We also establish a sum rule for the Landauer resistances of periodic structures formed by periodically repeating a basic subunit. Finally, we derive an analytical expression for the ‘‘boundary resistance’’ of a structure, as introduced by Azbel and Rubinstein in connection with pseudolocalization, and prove several properties of this quantity.

• Received 12 April 1990

DOI:https://doi.org/10.1103/PhysRevB.42.5100