Topological Hierarchy Insulators and Topological Fractal Insulators

TL;DR

This paper introduces topological hierarchy insulators (THIs), a new class of topological states combining parent insulators with defect-induced states, including self-similar fractal structures, and discusses potential experimental realizations.

Contribution

It proposes the concept of topological hierarchy insulators and topological fractal insulators, expanding the understanding of topological phases with defect-induced and self-similar structures.

Findings

Introduction of topological hierarchy insulators (THIs)

Identification of topological fractal insulators with self-similarity

Discussion of potential experimental realizations

Abstract

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.