Conductance calculations for quantum wires and interfaces: Mode matching and Green’s functions

Abstract

Landauer's formula relates the conductance of a quantum wire or interface to transmission probabilities. Total transmission probabilities are frequently calculated using Green's-function techniques and an expression derived by C. Caroli et al. [J. Phys. C 4, 916 (1971)]. Alternatively, partial transmission probabilities can be calculated from the scattering wave functions that are obtained by matching the wave functions in the scattering region to the Bloch modes of ideal bulk leads. An elegant technique for doing this, formulated by Ando [Phys. Rev. B 44, 8017 (1991)], is here generalized to any Hamiltonian that can be represented in tight-binding form. A more compact expression for the transmission matrix elements is derived, and it is shown how all the Green's function results can be derived from the mode-matching technique. We illustrate this for a simple model that can be studied analytically, and for an Fe\ensuremath{\mid}vacuum\ensuremath{\mid}Fe tunnel junction that we study using first-principles calculations.