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One-dimensional (1D) edge states formed at the boundaries of 2D normal andtopological insulators have shown intriguing quantum phases such as chargedensity wave and quantum spin Hall effect. Based on first-principlesdensity-functional theory calculations including spin-orbit coupling (SOC), weshow that the edge states of zigzag Sb(111) and Bi(111) nanoribbons drasticallychange the stability of their edge structures. For zigzag Sb(111) nanoribbon,the Peierls-distorted or reconstructed edge structure is stabilized by aband-gap opening. However, for zigzag Bi(111) nanoribbon, such two insulatingstructures are destabilized due to the presence of topologically protectedgapless edge states, resulting in the stabilization of a metallic,shear-distorted edge structure. We also show that the edge states of theBi(111) nanoribbon exhibit a larger Rashba-type spin splitting at the boundaryof Brillouin zone, compared to those of the Sb(111) nanoribbon. Interestingly,the spin textures of edge states in the Peierls-distorted Sb edge structure andthe shear-distorted Bi edge structure have all three spin componentsperpendicular and parallel to the edges, due to their broken mirror-planesymmetry. The present findings demonstrate that the topologically trivial andnontrivial edge states play crucial roles in determining the edge structures ofnormal and topological insulators.

Competing edge structures of Sb and Bi bilayers by trivial and nontrivial band topologies