9 SCIENTIFIC HIGHLIGHT OF THE MONTH: Calculating Scattering Matrices by Wave Function Matching Calculating Scattering Matrices by Wave Function Matching

As devices are reduced in size, interfaces start to dominate electrical transport making it essential to be able to describe reliably how they transmit and reflect electrons. Wave function matching (WFM) is a transparent technique for calculating transmission and reflection matrices suitable for any Hamiltonian that can be represented in tight-binding form. A firstprinciples Kohn-Sham Hamiltonian represented on a localized orbital basis or on a real space grid has such a form. WFM is based upon direct matching of the scattering-region wave function to the Bloch modes of the leads. In this paper we give a pedagogical introduction to WFM. We briefly discuss WFM for calculating the conductance of atomic wires, using a real space grid implementation. A tight-binding muffin-tin orbital implementation very suitable for studying spin-dependent transport in layered magnetic materials is illustrated by looking at spin-dependent transmission through ideal and disordered interfaces. 1 Calculating the scattering matrix from first principles Various methods have been developed for calculating the transmission of electrons through an interface (or a more extended scattering region) from first principles [1–15], or using as input electronic structures which were calculated from first principles [16–22]. Most are based upon a formulation for the conductance in terms of non-equilibrium Green’s functions (NEGF) [23] which reduces in the appropriate limit to the well known Fisher-Lee linear-response form [24] for the conductance of a finite disordered wire embedded between crystalline leads. An alternative technique, suitable for Hamiltonians that can be represented in tight-binding form, has been formulated by Ando [25] and is based upon direct matching of the scattering-