Improvement of accuracy in the wave-function-matching method for transport calculations

The wave-function-matching (WFM) technique for first-principles transport-property calculations was bettered by Sørensen et al. so as to exclude rapidly decreasing evanescent waves [Sørensen et al., Phys. Rev. B 77, 155301 (2008)]. In their method, the translational invariance of the transmission probability is not preserved when moving the matching planes between electrode and transition regions, and the sum of transmission and reflection probabilities does not agree with the number of transport channels in the transition region. The lack of the translational invariance is caused by the overlap of the layers between the electrode and transition regions. We reformulate the WFM method by removing the layer overlap, and the translational invariance of the transmission probability becomes preserved. On the other hand, the error in the sum of transmission and reflection probabilities is attributed to using pseudoinverses that is accompanied by the exclusion of rapidly decreasing evanescent waves. We introduce a formulation to calculate the transmission/reflection probability without the pseudoinverses, resulting in that the sum of the transmission and reflection probabilities exactly agrees with the number of channels, and the accuracy is largely improved. In addition, we prove that the accuracy in the transmission probability obtained by our WFM technique is comparable to that obtained by a nonequilibrium Green's function method. Furthermore, we carry out electron transport calculations on two-dimensional graphene sheets embedded with B-N line defects sandwiched between a pair of semi-infinite graphene electrodes and find the dependence of the electron transmission on the transverse momentum perpendicular to the transport direction.