Topological Corner States in Graphene by Bulk and Edge Engineering

Abstract

Two-dimensional higher-order topology is usually studied in (nearly) particle-hole symmetric models, so that an edge gap can be opened within the bulk one. But more often deviates the edge anticrossing even into the bulk, where corner states are difficult to pinpoint. We address this problem in a graphene-based ${\mathbb{Z}}_2$ topological insulator with spin-orbit coupling and in-plane magnetization both originating from substrates through a Slater-Koster multi-orbital model. The gapless helical edge modes cross inside the bulk, where is also located the magnetization-induced edge gap. After demonstrating its second-order nontriviality in bulk topology by a series of evidence, we show that a difference in bulk-edge onsite energy can adiabatically tune the position of the crossing/anticrossing of the edge modes to be inside the bulk gap. This can help unambiguously identify two pairs of topological corner states with nonvanishing energy degeneracy for a rhombic flake. We further find that the obtuse-angle pair is more stable than the acute-angle one. These results not only suggest an accessible way to "find" topological corner states, but also provide a higher-order topological version of "bulk-boundary correspondence".

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Cited by in corpus (6)

• Engineering topologically protected zero-dimensional interface end states in antiferromagnetic heterojunction graphene nanoflakes
• The General Principle behind Magnetization-induced Second-Order Topological Corner States in the Kane-Mele Model
• Chiral-Flux-Phase-Based Topological Superconductivity in Kagome Systems with Mixed Edge Chiralities
• Altermagnetism Induced Topological Phase Transitions in Kane-Mele Model
• Bulk-boundary-transport correspondence of the second-order topological insulators
• Ferroelectric polarization controlled orbital Hall conductivity in a higher-order topological insulator: \textit{d1T}-phase monolayer MoS${}_2$