First-principles transport calculation method based on real-space finite-difference nonequilibrium Green's function scheme
First-principles transport calculation method based on real-space finite-difference nonequilibrium Green's function scheme
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DOI：
10.1103/physrevb.86.195406
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发表时间：
2012-07
影响因子：
3.7
通讯作者：
T. Ono;Y. Egami;K. Hirose
中科院分区：
文献类型：
--
作者：
T. Ono;Y. Egami;K. Hirose
我们展示了一个有效的非平衡绿色函数输运计算程序的基础上的实空间有限差分方法。在实空间方法中，用于获得电极的自能项的矩阵的直接求逆在计算上是苛刻的，因为矩阵维数对应于电极的单元格中的网格点的数目，这比紧束缚方法中的位点的数目大得多。该过程使用的比例矩阵的overbridging边界匹配技术[物理评论B {\bf 67}，195315（2003）]，这是一对网格平面的波函数在匹配区域，大大减少了计算工作量，计算自能项，而不失去数学的严格性。此外，本方法还节省了Landauer-B“uttiker公式所需的半无限系统的绿色函数的计算时间。此外，紧凑的表达式，以联系绿色的功能和散射波函数，它提供了一个真实的空间图片的散射过程，介绍。最后给出了BN环与（9，0）碳纳米管连接的输运性质的计算结果。在界面处的波函数匹配揭示了波函数关于管轴的旋转对称性在电子输运中起着重要的作用。由于来自电极和去往电极的状态显示三重旋转对称性，因此波函数呈现五重对称性的费米能级附近的状态对通过BN环的电子输运没有贡献。
We demonstrate an efficient nonequilibrium Green's function transport calculation procedure based on the real-space finite-difference method. The direct inversion of matrices for obtaining the self-energy terms of electrodes is computationally demanding in the real-space method because the matrix dimension corresponds to the number of grid points in the unit cell of electrodes, which is much larger than that of sites in the tight-binding approach. The procedure using the ratio matrices of the overbridging boundary-matching technique [Phys. Rev. B {\bf 67}, 195315 (2003)], which is related to the wave functions of a couple of grid planes in the matching regions, greatly reduces the computational effort to calculate self-energy terms without losing mathematical strictness. In addition, the present procedure saves computational time to obtain Green's function of the semi-infinite system required in the Landauer-B\"uttiker formula. Moreover, the compact expression to relate Green's functions and scattering wave functions, which provide a real-space picture of the scattering process, is introduced. An example of the calculated results is given for the transport property of the BN ring connected to (9,0) carbon nanotubes. The wave function matching at the interface reveals that the rotational symmetry of wave functions with respect to the tube axis plays an important role in electron transport. Since the states coming from and going to electrodes show threefold rotational symmetry, the states in the vicinity of the Fermi level, whose wave function exhibits fivefold symmetry, do not contribute to the electron transport through the BN ring.