Construction of second-order topological phases protected by chiral symmetry

We investigate topological phase transitions of a model to construct two-dimensional second-order topological insulators protected by chiral symmetry. By the theory of the topological phase transitions, we propose second-order topological semimetallic and insulating phases with flat hinge bands in chiral-symmetric three-dimensional systems. We also demonstrate the various second-order topological phases by constructing a two-dimensional lattice model from the Su-Schrieffer-Heeger models and by stacking the lattice models.