Border states in heterosheets with hexagonal symmetry

We report first-principles electronic-structure calculations using local density approximation in density functional theory for hexagonally bonded hetero sheets BNCx consisting of graphite and boron-nitride strips. We find a class of electron states that are localized at borders of the heterosheet. Calculations for other heterosheets and homosheets, C, BN, and BC3, clarify universal features of the border states, edge states, and nearly-free-electron states. Electronic properties related to the border states in planer or tubular BNC, are discussed.