  Second order topological insulator can be engineered from two-dimensional
materials with strong spin-orbit coupling and in-plane Zeeman field. In
proximity to superconductor, topological superconducting phase could be induced
in the two-dimensional materials, which host Majorana corner modes at the
intersection between two zigzag edges. Two types of tight binding models in
hexagonal lattice, which include $p_{z}$ or $p_{x,y}$ orbit(s) in each lattice
site, are applied to engineer two-dimensional materials in topological
superconducting phase. In both models, the condition that induces the second
order topological superconductor requires nonuniform value of either in-plane
Zeeman fields or superconductor pairing parameters in two sublattices. The
finite size effect of the second model is weaker than that of the first model.

Superconductivity;Mesoscale and Nanoscale Physics