  We theoretically demonstrate that the second-order topological insulator with
robust corner states can be realized in two-dimensional $\mathbb{Z}_2$
topological insulators by applying an in-plane Zeeman field. Zeeman field
breaks the time-reversal symmetry and thus destroys the $\mathbb{Z}_2$
topological phase. Nevertheless, it respects some crystalline symmetries and
thus can protect the higher-order topological phase. By taking the Kane-Mele
model as a concrete example, we find that spin-helical edge states along zigzag
boundaries are gapped out by Zeeman field whereas in-gap corner state at the
intersection between two zigzag edges arises, which is independent on the field
orientation. We further show that the corner states are robust against the
out-of-plane Zeeman field, staggered sublattice potentials, Rashba spin-orbit
coupling, and the buckling of honeycomb lattices, making them experimentally
feasible. Similar behaviors can also be found in the well-known
Bernevig-Hughes-Zhang model.
