  In this paper we propose an analytical method to calculate the band
structures of graphene-like nanoribbons of the armchair type with arbitrary
line defects or uniaxial strains. The model is based on the tight-binding model
and the standing wave assumption for the armchair nanoribbons. It gives
accurate band results for large supercell systems. Within this method, we
analyze different local states near the line defect in the graphene and
boron-nitride nanoribbons. We also derive the analytical expression for the
local states in a semi-infinite graphene nanoribbon by this method and the
transfer matrix technique. The criteria condition for the local states in the
semi-infinite nanoribbons is also given.
