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

TL;DR

This paper introduces an efficient method combining the shifted COCG algorithm with NEGF and real-space finite-difference techniques to perform large-scale quantum transport calculations more accurately and with reduced computational cost.

Contribution

The paper presents a novel approach that significantly improves the efficiency of Green's function calculations in first-principles transport simulations using real-space finite-difference methods.

Findings

Efficient computation of Green's functions using shifted COCG reduces cost.

Successful large-scale transport calculation on a carbon nanotube system.

Method enables parallel computation without losing accuracy.

Abstract

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.