Higher-order topology in monolayer graphene

Abstract

We show that monolayer graphene intrinsically hosts higher-order topological corner states, in which electrons are localized topologically at atomic sizes. The emergence of the topological corner states in graphene is due to a nontrivial product of the Zak phases for two independent directions, which can be handily calculated graphically by using the bulk wavefunctions. We give an explicit expression that indicates the existence of topological corner states for various geometric edges and corner angles. We also demonstrate the nontrivial localization nature of the topological corner states in graphene by putting an imaginary onsite potential mask.

arXiv comment13 pages, 3 figures

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• Valley-dependent Corner States in Honeycomb Photonic Crystal without Inversion Symmetry
• Two-particle Berry phase mechanism for Dirac and Majorana Kramers pairs of corner modes
• Hidden Breathing Kagome Topology in Hexagonal Transition Metal Dichalcogenides
• Topological Edge and Corner States in Biphenylene Network
• Topological Corner States in Graphene by Bulk and Edge Engineering
• Bulk-boundary-transport correspondence of the second-order topological insulators
• Hierarchical Topological States in Thermal Diffusive Networks
• Additive rule of real and reciprocal space topologies at disclinations
• Intrinsic higher-order topological states in 2D honeycomb Z_2 quantum spin Hall insulators
• Josephson radiation patterns in underdamped topological Josephson junctions