Contour integral method for obtaining the self-energy matrices of electrodes in electron transport calculations

摘要

We propose an efficient computational method for evaluating the self-energymatrices of electrodes to study ballistic electron transport properties innanoscale systems. To reduce the high computational cost incurred for largesystems, a contour integral eigensolver based on the Sakurai-Sugiura methodcombined with the shifted biconjugate method is developed to solveexponential-type eigenvalue problem for complex wave vector. A remarkablefeature of the proposed algorithm is that the numerical procedure is verysimilar to that of e conventional band structure calculations, thereby enablingthe use of fast and sophisticated numerical techniques and allowing us toperform large scale electron transport calculations. We implement the developedmethod in the framework of the real-space higher-order finite difference schemewith nonlocal pseudopotentials. Numerical tests for a wide variety of materialsvalidate the robustness, accuracy, and efficiency of the proposed method; inall cases, this method achieves speed-up of up to three orders of magnitudecompared with the conventional method using the standard eigensolver.