Magnetic States of the Zigzag Edge of a Graphene Nanoribbon

Using a simple structural model and the multicenter Anderson Hamiltonian, Green's functions are obtained for the atoms of the zigzag edge of an epitaxial graphene nanoribbon. The electronic structure of the free nanoribbon is discussed in detail. Specifically, expressions for the band spectrum and density of states are found and estimates of the occupation numbers and magnetic moments are given. For a nanoribbon strongly bonded to a metal substrate, the criteria for the appearance of magnetic moments are determined. As it is shown for both free and epitaxial nanoribbons, the probability of the appearance of magnetic moments and their magnitude for zigzag edge atoms that have two nearest neighbors is higher than for atoms with three nearest neighbors.