A Mode-Matching Method for Multichannel Scattering Problems

We present a simple method for solving scattering problems with multiple incoming and outgoing channels and demonstrate its application to the problem of conduction through a ferromagnetic domain wall.We have been involved in theoretical research aimed at understanding the physics of electron transport through domain walls in nanowires [3,4].Here we consider the problem of electron scattering from a domain wall using a simple free-electron model in which the domain wall is represented as a spin-dependent potential.Taking the electron spin into account requires that we work with two-component spinor wavefunctions.This problem is analogous to one-dimensional potential scattering problems from elementary quantum mechanics, with the complication that the domain wall causes mixing between the two spinor components.There are thus multiple transmitted and reflected states.Although a variety of computational methods exist for such problems (for example, the recursive Green's function (RGF) algorithm), it is desirable to have an intuitive and simple method.We develop such a method in this article by extending the approach commonly used for the elementary one-dimensional problem. • Preliminary CodeFor the symbolic manipulations we perform in this article it is useful to modify the behaviour of the Equal function so that functions with the Listable attribute will be distributed across expressions with head Equal.