Model of impurity segregation in graphene nanoribbons

The electronic properties of low-dimensional materials can be engineered by doping, but in the case of graphene nanoribbons (GNRs) the proximity of two symmetry-breaking edges introduces an additional dependence on the location of an impurity across the width of the ribbon. This introduces energetically favorable locations for impurities, leading to a degree of spatial segregation in the impurity concentration. We develop a simple model to describe how the change in energy of a GNR system doped with a single impurity depends on the impurity position. The model is validated by comparing its findings with ab initio calculations. Although our results agree with previous works predicting the dominance of edge disorder in GNR, we argue that the distribution of adsorbed impurities across a ribbon may be controllable by external factors, namely, an applied electric field. We propose that this control over impurity segregation may allow manipulation and fine tuning of the magnetic and transport properties of GNRs.

Figure 1

Schematic drawings of GNR. Left (right) panel shows a small cross section of a 4-ZGNR (7-AGNR). Filled and hollow symbols represent the two distinct sublattices of a hexagonal structure. On each panel, numbered sites indicate the positions where impurities will be included either substitutionally or as an adatom. The arrows indicate the periodicity direction.

Figure 2

(Color online) Segregation function $\beta$ for substitutional impurities on different locations of a 6-ZGNR. Red squares indicate the results for the model calculations; black circles those for DFT calculations for Ti atoms. Hollow and filled symbols indicate which sublattice contains the substitutional replacement. Lines are guide to the eyes only.

Figure 3

(Color online) Segregation function $\beta$ for adsorbed atoms on a 30-ZGNR (left panels) and 35-AGNR (right panels) for two values of the Fermi energy: $E_F=0.0t$ (top panels) and $E_F=0.2t$ (bottom panels). The filled (blue) and unfilled (red) circles represent adsorption sites from the two distinct sublattices. The solid and dashed lines connect sites within a given sublattice. Here we have focused on the central region of both ribbons, but the reader should note that the edge sites, not shown here, are the most favorable adsorption sites

Figure 4

(Color online) The segregation function at the edge of a ribbon, ${\beta }_{edge}$, measures how favorable the edge site of a ribbon is as an adsorption site relative to the central site. When $E_F=0$, the edge site is far more favorable for both a 10-ZGNR (black, solid line) and 11-AGNR (red, dashed line). However by shifting $E_F$, the edge and central sites become more equally favorable, particularly in the case of ZGNRs. Also shown is the case of an adatom in the “hollow” configuration in a 30-ZGNR (blue, dot-dashed line). In this case the edge and central sites correspond to atoms adsorbed in the middle of a hexagon at the edge or at the center of the nanoribbon.