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We propose an efficient procedure to obtain Green's functions by combiningthe shifted conjugate orthogonal conjugate gradient (shifted COCG) method withthe nonequilibrium Green's function (NEGF) method based on a real-spacefinite-difference (RSFD) approach. The bottleneck of the computation in theNEGF scheme is matrix inversion of the Hamiltonian including the self-energyterms of electrodes to obtain perturbed Green's function in the transitionregion. This procedure first computes unperturbed Green's functions andcalculates perturbed Green's functions from the unperturbed ones using amathematically strict relation. Since the matrices to be inverted to obtain theunperturbed Green's functions are sparse, complex-symmetric and shifted for agiven set of sampling energy points, we can use the shifted COCG method, inwhich once the Green's function for a reference energy point has beencalculated, the Green's functions for the other energy points can be obtainedwith a moderate computational cost. We calculate the transport properties of aC$_{60}$@(10,10) carbon nanotube (CNT) peapod suspended by (10,10)CNTs as anexample of a large-scale transport calculation. The proposed scheme opens thepossibility of performing large-scale RSFD-NEGF transport calculations usingmassively parallel computers without the loss of accuracy originating from theincompleteness of the localized basis set.

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