  We investigate the energy dispersion of the edge states in zigzag silicene,
germanene and stanene nanoribbons with and without hydrogen termination based
on a multi-orbital tight-binding model. Since the low buckled structures are
crucial for these materials, both the $\pi$ and $\sigma$ orbitals have a strong
influence on the edge states, different from the case for graphene nanoribbons.
The obtained dispersion of helical edge states is nonlinear, similar to that
obtained by first-principles calculations. On the other hand, the dispersion
derived from the single-orbital tight-binding model is always linear.
Therefore, we find that the non-linearity comes from the multi-orbital effects,
and accurate results cannot be obtained by the single-orbital model but can be
obtained by the multi-orbital tight-binding model. We show that the
multi-orbital model is essential for correctly understanding the dispersion of
the edge states in tetragen nanoribbons with a low buckled geometry.

Mesoscale and Nanoscale Physics