Numerical solver for firstprinciples transport calculation based on realspace finitedifference method
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 realspace finitedifference (RSFD) approach. The bottleneck of the computation in the NEGF scheme is matrix inversion of the Hamiltonian including the selfenergy terms of electrodes to obtain the 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, complexsymmetric, 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 largescale transport calculation. The proposed scheme opens the possibility of performing largescale RSFDNEGF transport calculations using massively parallel computers without the loss of accuracy originating from the incompleteness of the localized basis set.
 Publication:

Physical Review E
 Pub Date:
 June 2015
 DOI:
 10.1103/PhysRevE.91.063305
 arXiv:
 arXiv:1502.00081
 Bibcode:
 2015PhRvE..91f3305I
 Keywords:

 02.60.x;
 61.48.De;
 73.63.b;
 73.23.Ad;
 Numerical approximation and analysis;
 Structure of carbon nanotubes boron nanotubes and closely related graphitelike systems;
 Electronic transport in nanoscale materials and structures;
 Ballistic transport;
 Physics  Computational Physics