Commensurability effect on the electronic structure of carbon nanostructures: Impact on supercell calculations in nanotubes

¹ School of Physics, Trinity College Dublin - Dublin 2, Ireland
² CRANN, Trinity College Dublin - Dublin 2, Ireland
³ Instituto de Física, Universidade Federal Fluminense - Niterói, RJ, Brazil
⁴ Departamento de Fisica, ICEx, Universidade Federal Fluminense - Volta Redonda, RJ, Brazil
⁵ Instituto de Física Teórica, Universidade Estadual Paulista (Unesp) - São Paulo, SP, Brazil
⁶ Department of Chemical Engineering, Massachusetts Institute of Technology - Cambridge, MA, USA

^(a) ferreirmtcd.ie

Received: 13 December 2016
Accepted: 20 February 2017

Abstract

Friedel oscillations are ubiquitous features seen in all impurity-doped metallic structures but in the case of graphene-like materials they are not so evident because the relevant wavelengths are perfectly commensurate with the lattice parameter. Here we demonstrate that this commensurability effect leads to a slow convergence of supercell-based total energy calculations in impurity-doped carbon nanotubes. We derive a mathematically transparent expression for the formation energy and identify a very distinctive dependence on the size of the supercell unit. We make use of this dependence through a simple extrapolation scheme to obtain density functional theory results with accuracy levels that would otherwise require enormously large unit cells.