  In recent years, low-dimensional materials with tetragonal $P4/nmm$
(orthorhombic $Pnma$) space group having square-net (chain-like) substructure
of $p$-block elements have been studied extensively. By using a
first-principles calculation and a two-sites $\otimes$ two-orbitals
tight-binding model, we construct the unified low-energy effective Hamiltonian
and the $\mathbb{Z}_{2}$ topological phase diagram for such materials with
different filling factors. Near the chemical potential, we show that the
staggered arrangement of ions at 2c (4c) site yields the virtual hopping that
have the same form with the second nearest-neighbor hopping between the
square-net (chain-like) ions. We show that this hybridization and low-symmetry
of the chain-like structure protects the quantum spin Hall insulator phase.
Finally, the second order spin-orbit coupling on top of the atomic spin-orbit
coupling is considered to clarify the origin of the non-zero Berry phase
signals reported in recent quantum oscillation experiments.
