Bound States in Second-order Topological Graphitic Structures

TL;DR

This paper proposes a design principle for creating second-order topological insulators in 2D graphitic structures, enabling the realization of protected corner states and massive localized states through edge engineering.

Contribution

It introduces a general framework for designing quadrupole insulators in graphitic materials by manipulating zigzag edge configurations and domain wall smoothness.

Findings

Identification of four topological classes of graphitic structures.

Emergence of topologically protected massless corner states at domain intersections.

Demonstration of massive localized states with non-zero angular momentum.

Abstract

Quadrupole insulators are a class of second-order topological insulators (SOTIs) that host zero-dimensional corner states within a two-dimensional bulk. Despite their unique properties, their realization in electronic systems on realistic material platforms remains rare. In this work, we present a general design principle to obtain quadrupole insulators based on two-dimensional graphitic structures. By engineering the positions and connections of zigzag edges, we identify four topological classes of graphitic structures. We show that topologically protected massless corner state emerge at the intersection of domains belonging to different topological classes. Crucially, by tuning the smoothness of the domain wall, we further demonstrate the appearance of additional massive localized states with non-zero angular momentum. Our results provide a practical framework for realizing experimentally accessible SOTIs and uncover the coexistence of both massless and massive bound states in two dimensions.