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Characterized by zigzag and armchair boundaries, the narrow ribbons displaythe very different characteristics in Hall conductivities. It is shown that themulti-band-crossings occur in the energy spectrum for armchair ribbons, and thenumber of them depends on the width of ribbons. Theoretically, it is predicatedthat the conductivities exhibit drastic sign reversals for narrow ribbons asthe Fermi energy sweep over the band-crossings. A new classification ofarmchair ribbons is suggested based on the emergence of a flat band in theenergy spectrum only for odd armchair ribbons. The evolution of jumped Hallconductivities to step-like plateaus and the restore of density of states atthe van Hove singularity in the limitation to graphene sheet have beenanalyzed.

Sign reversal of Hall conductivity and quantum confinement in graphene ribbons