  We design germanium-based higher-order topological cavities for terahertz
applications by breaking the symmetry of a two-dimensional photonic crystal
following the Su-Schrieffer-Heeger model. Calculations demonstrate the parity
inversion of the electric field in differently deformed unit cells. The
interface between domains of opposite topology presents edge and corner modes.
The former are chiral, locking light propagation to its helicity. The latter
prove that Ge-based structures can be used as high-order topological photonic
crystals. These findings can accelerate the development of Si-photonic
components working in a spectral range of high technological interest.
