Edge states of Bi nanoribbons on Bi substrates: First-principles density functional study

By using fully relativistic first-principles calculations, we study edge states of the Bi(001) nanoribbons. We find that freestanding zigzag bismuth nanoribbons (ZBNRs) have two spin degenerate bands around the Fermi energy, whose wave functions are localized at the edges. The wave functions are sharply localized at the edges at the zone boundary and become delocalized as the wave number decreases. In the case of the ZBNR on Bi substrates, the inversion symmetry is broken. As a result, the spin degenerate bands split and thus the density of states near the Fermi level has broad distributions; therefore, the electronic structures are expected to be stabilized. Because of the edge state near the Fermi energy, conduction along the edge lines is expected. However, the topological insulator predicted in the case of the freestanding ZBNR is not achieved in the case of the ZBNR on Bi substrates.