Tsukamoto Shigeru, Ono Tomoya, Hirose Kikuji, Blügel Stefan
Peter Grünberg Institut & Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, D-52425 Jülich, Germany.
Center for Computational Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8577, Japan.
Phys Rev E. 2017 Mar;95(3-1):033309. doi: 10.1103/PhysRevE.95.033309. Epub 2017 Mar 20.
The self-energy term used in transport calculations, which describes the coupling between electrode and transition regions, is able to be evaluated only from a limited number of the propagating and evanescent waves of a bulk electrode. This obviously contributes toward the reduction of the computational expenses in transport calculations. In this paper, we present a mathematical formula for reducing the computational expenses further without using any approximation and without losing accuracy. So far, the self-energy term has been handled as a matrix with the same dimension as the Hamiltonian submatrix representing the interaction between an electrode and a transition region. In this work, through the singular-value decomposition of the submatrix, the self-energy matrix is handled as a smaller matrix, whose dimension is the rank number of the Hamiltonian submatrix. This procedure is practical in the case of using the pseudopotentials in a separable form, and the computational expenses for determining the self-energy matrix are reduced by 90% when employing a code based on the real-space finite-difference formalism and projector-augmented wave method. In addition, this technique is applicable to the transport calculations using atomic or localized basis sets. Adopting the self-energy matrices obtained from this procedure, we present the calculation of the electron transport properties of C_{20} molecular junctions. The application demonstrates that the electron transmissions are sensitive to the orientation of the molecule with respect to the electrode surface. In addition, channel decomposition of the scattering wave functions reveals that some unoccupied C_{20} molecular orbitals mainly contribute to the electron conduction through the molecular junction.
输运计算中使用的自能项描述了电极与过渡区域之间的耦合，它只能从体电极的有限数量的传播波和倏逝波中进行评估。这显然有助于降低输运计算中的计算成本。在本文中，我们提出了一个数学公式，可在不使用任何近似且不损失精度的情况下进一步降低计算成本。到目前为止，自能项一直被处理为一个与表示电极和过渡区域之间相互作用的哈密顿子矩阵具有相同维度的矩阵。在这项工作中，通过子矩阵的奇异值分解，自能矩阵被处理为一个较小的矩阵，其维度是哈密顿子矩阵的秩数。在使用可分离形式的赝势的情况下，该过程是实用的，并且当采用基于实空间有限差分形式和投影增强波方法的代码时，确定自能矩阵的计算成本降低了90%。此外，该技术适用于使用原子或局域基组的输运计算。采用从该过程获得的自能矩阵，我们给出了C₂₀分子结电子输运性质的计算。该应用表明电子传输对分子相对于电极表面的取向敏感。此外，散射波函数的通道分解表明，一些未占据的C₂₀分子轨道主要对通过分子结的电子传导有贡献。
