  We study the interplay between the edge states and a single impurity in a
zigzag graphene nanoribbon. We use tight-binding exact diagonalization
techniques, as well as density functional theory calculations to obtain the
eigenvalue spectrum, the eigenfunctions, as well the dependence of the local
density of states (LDOS) on energy and position. We note that roughly half of
the unperturbed eigenstates in the spectrum of the finite-size ribbon hybridize
with the impurity state, and the corresponding eigenvalues are shifted with
respect to their unperturbed values. The maximum shift and hybridization occur
for a state whose energy is inverse proportional to the impurity potential;
this energy is that of the impurity peak in the DOS spectrum. We find that the
interference between the impurity and the edge gives rise to peculiar
modifications of the LDOS of the nanoribbon, in particular to oscillations of
the edge LDOS. These effects depend on the size of the system, and decay with
the distance between the edge and the impurity.
