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| In this paper, we investigate the finite sizeeffect of helical edge states on the Lieb lattice with ISO coupling underthree different kinds of boundary conditions, i.e., the straight, beardedand asymmetry edges. The spectrum and wave function of edge modes arederived analytically for a tight-binding model on the Lieb lattice. For a strip Lieb lattice with two straight edges, the ISOcoupling induces the Dirac-like bulk states to localize at the edges tobecome the helical edge states with the same Dirac-like spectrum. Moreover,it is found that in the case with two straight edges the gapless Dirac-likespectrum remains unchanged with decreasing the width of the strip Lieblattice, and no gap is opened in the edge band, that is, finite size effectof QSH states is absent. However, in the other two cases with the beardedand asymmetry edges, the energy gap induced by finite size effect is stillopened with decreasing the width of the strip. |
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| Keywords:quantum spin Hall state; finite size effect; spin-orbit coupling; topological insulators |
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