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.

13 pages, 3 figures

References in corpus (14)

• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices
• Quantum Spin Hall Effect and Topologically Invariant Chern Numbers
• Direct observation of corner states in second-order topological photonic crystal slabs
• Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators
• Novel Topological Phase with Zero Berry Curvature
• Photonic crystal nanocavity based on a topological corner state
• Low-threshold topological nanolasers based on second-order corner state
• Realization of an acoustic third-order topological insulator
• Higher-Order Weyl Semimetals
• Higher-order Weyl Semimetals
• Edge Effect on Electronic Transport Properties of Graphene Nanoribbons and Presence of Perfectly Conducting Channel
• Topological states in non-Hermitian two-dimensional Su-Schrieffer-Heeger model

Cited by in corpus (13)

• $C_n$-symmetric higher-order topological crystalline insulators in atomically thin transition-metal dichalcogenides
• Unconventional Materials: the mismatch between electronic charge centers and atomic positions
• Second Order Topological Insulator State in Hexagonal Lattices and its Abundant Material Candidates
• 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