Calculation of the residual resistivity of three-dimensional quantum wires

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Abstract
An exact scattering theory formulation of the elastic transport problem is used in a 1s tight-binding implementation to calculate the zero-temperature elastic resistances of disordered three-dimensional quantum wires with cross sections as large as 14×14 atoms and lengths of up to hundreds of atoms. A real-space Green function technique is used to construct the wires. The technique is flexible and simple to implement, making it possible to study a range of different geometries, types of disorder, and combinations thereof. The possible use of such calculations to evaluate the bulk residual resistivity of the respective materials is outlined. Attention is given to the statistics and the configurational averaging of the calculated results. The transition from the Ohmic to the localization regime in the wires is also studied. The shape of this transition, obtained from the numerical results, is found to correspond well to a curious semiempirical analytic form. Model calculations with different types of on-site disorder, and with interfacial roughness, combined with impurity scattering, are presented at the end. © 1996 The American Physical Society.