Second-order topological corner states in zigzag graphene nanoflake with different types of edge magnetic configurations

Abstract

We study the energy spectrum and energy levels of the extended Kane-Mele model with magnetic atoms on their zigzag edges. It is demonstrated that the edges of ferromagnetism or antiferromagnetism are enough to break the time-reversal symmetry and host one-dimensional gapped edge states. Thus, a second-order topological phase transition could happen, which leads to the emergence of topological in-gap zero-dimensional corner states. We also prove that the in-gap corner states are robust against corner defects and magnetic disorder. Our proposal based on the edge antiferromagnetism shows that the high-order topological states can be realized, although the net magnetization of the material is zero. In addition, we discuss the influence of spin magnetization orientation on the degeneracy and energy of in-gap corner states.

9 pages, 8 figures

References in corpus (62)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Energy Gaps in Graphene Nanoribbons
• Classification of topological quantum matter with symmetries
• Quantized Electric Multipole Insulators
• Higher-Order Topological Insulators
• Colloquium: Topological Band Theory
• 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
• Topolectrical circuit realization of topological corner modes
• Reflection symmetric second-order topological insulators and superconductors
• Observation of a phononic quadrupole topological insulator
• Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices
• Acoustic higher-order topological insulator on a Kagome lattice
• Demonstration of a quantized microwave quadrupole insulator with topologically protected corner states
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Room temperature magnetic order on zigzag edges of narrow graphene nanoribbons
• Atomic-scale control of graphene magnetism using hydrogen atoms
• Visualization of higher-order topological insulating phases in two-dimensional dielectric photonic crystals
• Direct observation of corner states in second-order topological photonic crystal slabs
• Higher-order topological insulators and superconductors protected by inversion symmetry
• Topological Phases in Two-Dimensional Materials: A Brief Review
• Spin transport in proximity induced ferromagnetic graphene
• Magnetic Insulator-Induced Proximity Effects in Graphene: Spin Filtering and Exchange Splitting Gaps
• Two-dimensional second-order topological insulator in graphdiyne
• Chiral voltage propagation in a self-calibrated topolectrical Chern circuit
• Bulk-boundary correspondence of topological insulators from their Green's functions
• Symmetry indicators and anomalous surface states of topological crystalline insulators
• Dirac Fermions in Antiferromagnetic Semimetal
• Realization of an acoustic third-order topological insulator
• Minimal model for higher-order topological insulators and phosphorene
• Demonstration of a 3rd order hierarchy of higher order topological states in a three-dimensional acoustic metamaterial
• Engineering Corner States from Two-Dimensional Topological Insulators
• Carrier Density and Magnetism in Graphene Zigzag Nanoribbons
• Mechanical Weyl Modes in Topological Maxwell Lattices
• Non-Hermitian higher-order topological states in nonreciprocal and reciprocal systems with their electric-circuit realization
• Boundary Green functions of topological insulators and superconductors
• Topological switch between second-order topological insulators and topological crystalline insulators
• Dirac Fermions in Antiferromagnetic FeSn Kagome Lattices with Combined Space Inversion and Time Reversal Symmetry
• Majorana corner and hinge modes in second-order topological insulator-superconductor heterostructures
• Square-root higher-order topological insulator on a decorated honeycomb lattice
• Braiding of Majorana corner states in electric circuits and its non-Hermitian generalization
• $C_n$-symmetric higher-order topological crystalline insulators in atomically thin transition-metal dichalcogenides
• Higher-order topological phases in a spring-mass model on a breathing kagome lattice
• Higher Order Topological Insulator via Periodic Driving
• Floquet Second-Order Topological Superconductor Driven via Ferromagnetic Resonance
• The Hubbard model on the honeycomb lattice: from static and dynamical mean-field theories to lattice quantum Monte Carlo simulations
• Multi-orbital model reveals second-order topological insulator in 1H-transition metal dichalcogenide
• Quantum Monte Carlo studies of edge magnetism in chiral graphene nanoribbons
• Corner states and topological transitions in two-dimensional higher-order topological sonic crystals with inversion symmetry
• Higher-Order Topological Phase in a Honeycomb-Lattice Model with Anti-Kekulé Distortion
• A Higher-Order Topological Insulator Phase in a Modulated Haldane Model
• Bulk-boundary correspondence in three dimensional topological insulators
• Edge magnetism impact on electrical conductance and thermoelectric properties of graphenelike nanoribbons
• Impurity bound states as detectors of topological band structures revisited
• Spin-caloritronic transport in hexagonal graphene nanoflakes
• Valley Edelstein Effect in Monolayer Transition Metal Dichalcogenides
• Topological edge states of a graphene zigzag nanoribbon with spontaneous edge magnetism
• Spin-triplet superconductor$-$quantum anomalous Hall insulator$-$spin-triplet superconductor Josephson junctions: $0$-$\pi$ transition, ${\varphi }_0$ phase and switch effects
• Spectral properties of Co-decorated quasi 2-dimensional GaSe layer

Cited by in corpus (8)

• Engineering second-order topological insulators via coupling two first-order topological insulators
• 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
• Interlayer Coupling Induced Topological Phase Transition to Higher Order
• Two-Dimensional Higher-Order Topological Metals
• Effects of first- and second-order topological phases on equilibrium crystal shapes
• Quantum spin Hall effect in bilayer honeycomb lattices with C-type antiferromagnetic order
• Engineering Two-Dimensional Hybrid-Order Topological Insulators via Trilayer Coupling