Linear augmented cylindrical wave Green’s function method for electronic structure of nanotubes with substitutional impurities

Abstract

A first-principles numerical method for calculation of the electronic structure of the point impurities in the single-walled carbon nanotubes (SWNTs) based on a Green's function technique is developed. The host SWNTs electron Green's function is calculated using a linear augmented cylindrical wave theory. The Green's function of the impurities is calculated in the terms of matrix Dyson equation. The impurities are described by the single-site perturbed muffin-tin potentials in otherwise perfect nanotubes with the rotational and helical symmetries. Due to the account of these symmetry properties, the method is developed applicable to any tubule including the chiral SWNTs with point defects independent of the number of atoms in translational unit cell of the host systems. We give results for the local densities of states (DOSs) of the boron and nitrogen impurities in the metallic (7,7), (5,5), and (10,10) semimetallic (8,2) and (9,6), and semiconducting (13,0), (12,2), (11,3), (10,5), (8,7), and (10,0) SWNTs, as well as in the polyynic and cumulenic carbynes. It is shown that the boron and nitrogen defects do not destroy the metallic character of electronic structure of the armchair tubules. An increase in the DOS in the Fermi energy region is the most significant effect of boron and nitrogen dopants in the case of metallic and semimetallic SWNTs. In all the semiconducting SWNTs, in the vicinity of optical gap, there is a drastic difference between the effects of the boron and nitrogen impurities. The boron-related states close the gap of the perfect tubules. In the gap region, the effects of nitrogen atom are restricted with a minor growth of the local DOSs just below and above the Fermi energy. Beyond the Fermi-energy region up to the $s$ bottom of the valence bands, the effects of impurities are similar in all the tubules. As one goes from carbon to the boron, the local DOS decreases, and the peaks almost disappear, but the nitrogen local DOS is somewhat greater than that of the carbon. In the semiconducting polyynic carbyne, the boron and nitrogen defects close the gap between the valence and conduction bands. In the case of metallic cumulenic carbine, if the boron or nitrogen atom takes the place of carbon, the local DOS at the Fermi level increases.