Improvement of accuracy of wave-function-matching technique for first-principles electron-transport calculation

The wave-function-matching (WFM) technique for first-principles transport-property calculations was modified by Sørensen et al. so as to exclude rapidly decreasing evanescent waves [Sørensen et al., Phys. Rev. B 77, 155301 (2008)]. However, this method lacks translational invariance of the transmission probability with respect to insertion of matching planes and consistency between the sum of the transmission and reflection probabilities and the number of channels in the transition region. We reformulate the WFM method since the original methods are formulated to include all the generalized Bloch waves and find that the translational invariance is destroyed by the pseudoinverses used to exclude the rapidly decreasing evanescent waves. We then devise a method that calculates the transmission probability without the pseudoinverses. As a result, we find that the translational invariance is properly retained. In addition, we prove that the accuracy in the transmission probability of this WFM technique is comparable with that obtained by the nonequilibrium Green's function method. As an example of the proposed method, we introduce an application for the electron transport property of nanostructures.