  This paper presents a systematic study of two and one dimensional honeycomb
structure of boron nitride (BN) using first-principles plane wave method.
Two-dimensional (2D) graphene like BN is a wide band gap semiconductor with
ionic bonding. Phonon dispersion curves demonstrate the stability of 2D BN
flakes. Quasi 1D armchair BN nanoribbon are nonmagnetic semiconductors with
edge states. Upon passivation of B and N with hydrogen atoms these edge states
disappear and band gap increases. Bare zigzag BN nanoribbons are metallic, but
become a ferromagnetic semiconductor when their both edges are passivated with
hydrogen. However, their magnetic ground state, electronic band structure and
band gap are found to be strongly dependent on whether B- or N-edge of the
ribbon is saturated with hydrogen. Vacancy defects in armchair and zigzag
nanoribbons affects also magnetic state and electronic structure. In order to
reveal dimensionality effects these properties are contrasted with those of
various 3D BN crystals and 1D BN atomic chain.
