Improvement of accuracy of wave-function-matching method for transport calculation

TL;DR

This paper improves the wave-function-matching method for quantum transport calculations by removing layer overlaps and pseudoinverses, ensuring invariance and probability sum rules, and demonstrates its effectiveness on graphene with B-N defects.

Contribution

The authors reformulate the wave-function-matching method to enhance accuracy, invariance, and probability consistency, addressing limitations of previous approaches.

Findings

The new method retains translational invariance of transmission probabilities.

The sum of transmission and reflection probabilities matches the number of channels.

The method's accuracy is comparable to the nonequilibrium Green's function approach.

Abstract

The wave-function-matching (WFM) technique for first-principles transport-property calculations was modified by S\o{}rensen {\it et al.} so as to exclude rapidly decreasing evanescent waves [S\o{}rensen {\it et al.}, Phys. Rev. B {\bf 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. It is found that the translational invariance is destroyed by the overlap of the layers between the electrode and transition regions and by the pseudoinverses used to exclude the rapidly decreasing evanescent waves. We then devise a method that removes the overlap and calculates the transmission probability without the pseudoinverses. As a result, we find that the translational invariance of the transmission probability with respect to insertion of the extra layers is properly retained and the sum of the transmission and reflection probabilities exactly agrees with the number of channels. 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. Furthermore, we carry out the 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 direction of transport.