Removing all periodic boundary conditions: Efficient nonequilibrium Green's function calculations

Abstract

We describe a method and its implementation for calculating electronic structure and electron transport without approximating the structure using periodic super-cells. This effectively removes spurious periodic images and interference effects. Our method is based on already established methods readily available in the non-equilibrium Green function formalism and allows for nonequilibrium transport. We present examples of a N defect in graphene, finite voltage bias transport in a point-contact to graphene, and a graphene-nanoribbon junction. This method is less costly, in terms of CPU-hours, than the super-cell approximation.

Siesta: Recent developments and applications

“…It is based on the non-equilibrium Green function formalism which allows biased calculations. TRAN-SIESTA has been completely re-written and now uses advanced inversion algorithms, enables N e ≥ 1 electrodes, allows thermo-electric calculations, performing real-space calculations (without k-points) and adds phonon transport calculations using the Hessian 98,99 ,…”

“…A recent addition to the TRANSIESTA package is the use of real space self-energy terms 99,103 . These self-energies are semi-infinite in more than 1 direction and can thus be used as surrounding electrodes, for e.g.…”

“…Real space self-energies are superior to BZ integrated quantities since they correctly describe the infinite bulk by leaving out image couplings and also removes the need for k-point sampling. When taking into account the complete procedure for a TRANSIESTA calculation the real space self-energies provide an increased throughput since the SCF k-point sampling and the subsequent k-point sampled transport calculation are completely removed 99 .…”

Electrostatic superlattices on scaled graphene lattices

“…The method can be immediately applied to take into account, for example, complex local gating or multi-probe transport, in order to make further analysis for transport experiments or even reliable predictions. We note some recent studies working on developing numerical techniques that allow large-scale efficient transport simulations [47][48][49], but scaling the graphene lattices with an appropriately chosen scaling factor depending on the superlattice periodicity seems to be of least technical complexity and is readily applicable to anyone who is familiar with quantum transport using, for example, real-space Green's function method [32] or the popular open-source python package KWANT [50].…”

Electric-Field Control of a Single-Atom Polar Bond

“…The density-functional and transport calculations (see Supplemental Material [11]) were carried out for a simplified quasi-one-dimensional Au tip on top of a free finite graphene sheet [Fig. 3(a)] [13,14]. They showed that the relaxation of the junction geometry prefers the top-C position to the hollow (by ≈0.2 eV) and bridge (by ≈0.04 eV) site of the graphene honeycomb cell.…”