  The Hopf insulators are characterized by a topological invariant called Hopf
index which classifies maps from three-sphere to two-sphere, instead of a Chern
number or a Chern parity. In contrast to topological insulator, the Hopf
insulator is not protected by any kind of symmetry. By dimensional reduction,
we argue that there exists a new type of $\mathbb{Z}_2$ index for 2D
Hamiltonian with vanishing Chern number. Specific model Hamiltonian with this
nontrivial $\mathbb{Z}_2$ index is constructed. We also numerically calculate
the topological protected edge modes of this dimensional reduced Hopf insulator
and show that they are consistent with the $\mathbb{Z}_2$ classification.
