标题： 基于实空间有限差分方法的第一性原理输运计算的高效数值求解器 显示英文标题

标题： Efficient numerical solver for first-principles transport calculation based on real-space finite-difference method

摘要： 我们提出了一种高效的程序，通过将位移共轭正交共轭梯度（位移 COCG）方法与基于实空间有限差分（RSFD）方法的非平衡格林函数（NEGF）方法相结合，以获得格林函数。 NEGF方案中的计算瓶颈是矩阵求逆，即在包含电极自能项的哈密顿量中，以获得过渡区域中的扰动格林函数。 该过程首先计算未受扰的格林函数，并使用数学上严格的关系从未受扰的格林函数中计算出扰动格林函数。 由于为了获得未受扰的格林函数而需要求逆的矩阵是稀疏的、复对称的，并且对于给定的一组采样能量点是位移的，因此我们可以使用位移 COCG 方法，其中一旦计算了参考能量点的格林函数，就可以以适度的计算成本获得其他能量点的格林函数。 我们以一个由（10,10）CNT 悬挂的 C$_{60}$@(10,10) 碳纳米管（CNT）豆荚为例，计算其输运特性，作为大规模输运计算的一个例子。 所提出的方案为使用大规模并行计算机进行大规模 RSFD-NEGF 输运计算提供了可能性，而不会因局域基组的不完整性而导致精度损失。 显示英文摘要

摘要： We propose an efficient procedure to obtain Green's functions by combining the shifted conjugate orthogonal conjugate gradient (shifted COCG) method with the nonequilibrium Green's function (NEGF) method based on a real-space finite-difference (RSFD) approach. The bottleneck of the computation in the NEGF scheme is matrix inversion of the Hamiltonian including the self-energy terms of electrodes to obtain perturbed Green's function in the transition region. This procedure first computes unperturbed Green's functions and calculates perturbed Green's functions from the unperturbed ones using a mathematically strict relation. Since the matrices to be inverted to obtain the unperturbed Green's functions are sparse, complex-symmetric and shifted for a given set of sampling energy points, we can use the shifted COCG method, in which once the Green's function for a reference energy point has been calculated, the Green's functions for the other energy points can be obtained with a moderate computational cost. We calculate the transport properties of a C$_{60}$@(10,10) carbon nanotube (CNT) peapod suspended by (10,10)CNTs as an example of a large-scale transport calculation. The proposed scheme opens the possibility of performing large-scale RSFD-NEGF transport calculations using massively parallel computers without the loss of accuracy originating from the incompleteness of the localized basis set.