Jesper Toft Rasmussen and Mads Brandbyge, Center for Nanostructured Graphene (CNG), Department of Micro- and Nanotechnology (DTU Nanotech), Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark 
 
Calculations of electronic conductance based on first principle methods provide a parameter-free route to assessing the scattering properties of extended defects in graphene such as grain boundaries [1] or adsorbate structures [2]. Typically these are treated employing periodic boundary conditions in the direction transverse to the transport direction and a corresponding k-point average. It is well-known that in order to obtain smooth and converged DOS and transmissions as a function of energy a substantial number of transverse k-points are needed due to the rapid variations of the functions for individual k-points. This can amount to a significant computational burden for large systems treated by first principle methods such as DFT-NEGF. 

Here we present a simple interpolation scheme which can significantly speed up the convergence with k-points of DOS and transmission calculations through nanostructured systems. We apply our interpolation scheme to several test cases: (i) pristine graphene (see Fig. 1a), (ii) graphene with hydrogenation along a line (“kinked graphene”) [2] (see Fig. 1b), and (iii) graphene nano-constrictions [3]. The three mentioned cases show the diversity of the interpolation scheme, and its potential to reduce computation time. The outcome is shown in Fig. 2. Finally, we address the intrinsic limitations.

[1] Yazyev and Louie, Nature Materials, 9 (2010) 806.
[2] Rasmussen et al., Beilstein J. Nanotechnol., 4 (2013) 103.
[3] Gunst et al., Phys. Rev. B, 88 (2013) 161401. 

Jesper Toft Rasmussen obtained his MSE degree in Physics and nanotechnology from the Technical University of Denmark in 2012. He is currently a Ph.D. student in the theoretical nanoelectronics group lead by Assoc. Prof. Mads Brandbyge. His main research interests are electronic and transport properties as well as chemical functionalization covering subjects such as graphene-hydrogen interaction, reactivity and non-planar graphene-based structures.