  The electronic properties of low-dimensional materials can be engineered by
doping, but in the case of graphene nanoribbons (GNR) 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 calculate the
change in energy of a GNR system with an arbitrary impurity as that impurity is
moved across the ribbon and validate its findings by comparison 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.
