▎ 摘　　要

Electronic edge ("surface") states are investigated in semi-infinite graphene sheets and graphene ribbons (monolayers) with armchair, zig-zag or horseshoe edges within the nearest-neighbour tight-binding approximation. The problem is generalized to include edge elements of the hopping (transfer) matrix which are distinct from the infinite-sheet ("bulk") ones. Within this model the semi-infinite graphene sheets with zig-zag or horseshoe edges exhibit edge states, while the semi-infinite graphene sheet with armchair edge does not. The energy of the edge states derived here lies above the (zero) Fermi level. Similarly, symmetric graphene ribbons with zig-zag or horseshoe edges have edges states, while ribbons with asymmetric edges (zig-zag and horseshoe) have not. It is also shown how to construct the "reflected" solution for the intervening equations with finite differences both for semi-infinite sheets and ribbons, either with uniform matrix elements or with modified elements of the hopping matrix at the edges.