Energy gaps and half-metallicity in β-graphyne nanoribbons

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We investigate the energy gaps and half-metallicity of the zigzag-edged β-graphyne nanoribbons via a tight-binding approach. In the presence of on-site Coulomb repulsion and proper transverse electric field strengths, the nanoribbons are forced into a half-metallic state by the electric field. A phase transition from half-metal to insulator is realized by changing the electric field or Coulomb potential. Both the electric field and Coulomb repulsion can open direct band gaps, resulting in a metal-insulator phase transition. The band gaps oscillate with the electric field, contrary to linear change with the Coulomb potential.