Efficient implementation of the nonequilibrium Green function method for electronic transport calculations

TL;DR

This paper presents an efficient implementation of the nonequilibrium Green function method combined with density functional theory for electronic transport calculations, improving accuracy and computational speed for complex systems.

Contribution

The authors develop novel methods for evaluating the density matrix and boundary treatment, enhancing efficiency and precision in NEGF-DFT calculations for various nanostructures.

Findings

Rapid convergence of the density matrix demonstrates computational efficiency.

Successful application to graphene nanoribbons, tunneling junctions, and superlattices.

Accurate boundary treatment reduces spurious scattering effects.

Abstract

An efficient implementation of the nonequilibrium Green function (NEGF) method combined with the density functional theory (DFT) using localized pseudo-atomic orbitals (PAOs) is presented for electronic transport calculations of a system connected with two leads under a finite bias voltage. In the implementation, accurate and efficient methods are developed especially for evaluation of the density matrix and treatment of boundaries between the scattering region and the leads. Equilibrium and nonequilibrium contributions in the density matrix are evaluated with very high precision by a contour integration with a continued fraction representation of the Fermi-Dirac function and by a simple quadratureon the real axis with a small imaginary part, respectively. The Hartree potential is computed efficiently by a combination of the two dimensional fast Fourier transform (FFT) and a finite difference method, and the charge density near the boundaries is constructed with a careful treatment to avoid the spurious scattering at the boundaries. The efficiency of the implementation is demonstrated by rapid convergence properties of the density matrix. In addition, as an illustration, our method is applied for zigzag graphene nanoribbons, a Fe/MgO/Fe tunneling junction, and a LaMnO$_3/$SrMnO$_3$ superlattice, demonstrating its applicability to a wide variety of systems.