  Topological insulators are new states of quantum matter with metallic
edge/surface states. In this paper, we pointed out that there exists a new type
of particle-hole symmetry-protected topological insulator - topological
hierarchy insulator (THI), a composite topological state of a (parent)
topological insulator and its defect-induced topological mid-gap states. A
particular type of THI is topological fractal insulator, that is a THI with
self-similar topological structure. In the end, we discuss the possible
experimental realizations of THIs.
