Kagome edge states under lattice termination, spin-orbit coupling, and magnetic order

Abstract

We study the edge state properties of a two-dimensional kagome lattice using a tight-binding approach, focusing on the role of lattice termination, spin-orbit coupling, and magnetic order. In the pristine limit, we show that the existence of localized edge states is highly sensitive to boundary geometry, with certain terminations completely suppressing edge modes. Kane-Mele spin-orbit coupling opens a bulk gap and stabilizes topologically protected helical edge states, yielding a robust ${\mathbb{Z}}_2$ insulating phase that is insensitive to termination details. In contrast, the combined effect of a Zeeman field and Rashba spin-orbit coupling drives the system into Chern insulating phases, with Chern numbers consistent with the number of chiral edge modes. We further demonstrate that non-coplanar magnetic textures generate multiple Chern phases through finite scalar spin chirality, with Kane-Mele coupling strongly tuning the topological gaps. Our results provide important insights into the tunability of edge states in the kagome lattice, which can be key to designing materials with novel electronic properties and topological phases.

main text: 16 pages, 7 figures. supplement: 3 page, 3 figures

References in corpus (73)

• The electronic properties of graphene
• Quantum Spin Hall Effect in Graphene
• Fault-tolerant quantum computation by anyons
• Non-Abelian Anyons and Topological Quantum Computation
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Anomalous Hall effect
• Half-Metallic Graphene Nanoribbons
• Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Quantized Anomalous Hall Effect in Magnetic Topological Insulators
• Giant anomalous Hall effect in a ferromagnetic Kagome-lattice semimetal
• Fractionalized excitations in the spin liquid state of a kagomé lattice antiferromagnet
• Majorana Zero Modes and Topological Quantum Computation
• CsV${}_3$Sb${}_5$: a ${\mathbb{Z}}_2$ topological kagome metal with a superconducting ground state
• Massive Dirac fermions in a ferromagnetic kagome metal
• Anomalous Hall effect in ferromagnetic semiconductors
• An equivalent expression of Z2 Topological Invariant for band insulators using Non-Abelian Berry's connection
• Quantum Anomalous Hall Effect in Graphene from Rashba and Exchange Effects
• Spin Anisotropy and Quantum Hall Effect in the Kagome Lattice - Chiral Spin State based on a Ferromagnet-
• Roton pair density wave and unconventional strong-coupling superconductivity in a topological kagome metal
• Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
• Evidence for Magnetic Weyl Fermions in a Correlated Metal
• Computing topological invariants without inversion symmetry
• Discovery of a quantum limit Chern magnet TbMn6Sn6
• Time-reversal symmetry-breaking charge order in a kagome superconductor
• Charge density waves and electronic properties of superconducting kagome metals
• Superconductivity in the ${\mathbb{Z}}_2$ kagome metal KV${}_3$Sb${}_5$
• Wannier representation of Z_2 topological insulators
• Skyrmion phase and competing magnetic orders on a breathing kagome lattice
• Ising models of quantum frustration
• Fractionalization in an Easy-axis Kagome Antiferromagnet
• Time-reversal-symmetry-broken quantum spin Hall effect
• Discovery of charge density wave in a correlated kagome lattice antiferromagnet
• Magnetic and Electronic Properties of Metal-Atom Adsorbed Graphene
• Symmetry breaking due to Dzyaloshinsky-Moriya interactions in the kagome lattice
• Chirality driven anomalous Hall effect in weak coupling regime
• Three-state nematicity and magneto-optical Kerr effect in the charge density waves in kagome superconductors
• Spin waves in the Frustrated Kagome Lattice Antiferromagnet KFe3(OH)6(SO4)2
• Tunable nodal kagome superconductivity in charge ordered RbV3Sb5
• Charge-order-assisted topological surface states and flat bands in the kagome superconductor CsV${}_3$Sb${}_5$
• Topological states on the breathing kagome lattice
• Topological Lifshitz transitions
• Spontaneous topological Hall effect induced by non-coplanar antiferromagnetic order in intercalated van der Waals materials
• Discovery of charge order and corresponding edge state in kagome magnet FeGe
• Magnon thermal Hall effect in kagome antiferromagnets with Dzyaloshinskii-Moriya interactions
• The Heisenberg antiferromagnet on the kagome lattice with arbitrary spin: A high-order coupled cluster treatment
• Large anomalous Hall effect in the kagome ferromagnet LiMn${}_6$Sn${}_6$
• Ferromagnetism in single-band Hubbard models with a partially flat band
• Novel magnetic orderings in the kagome Kondo-lattice model
• Magnetic Structure and Spin Waves in the Kagomé Jarosite compound $\mathbf{KF}{\mathbf{e}}_3(\mathbf{S}{\mathbf{O}}_4{)}_2(\mathbf{OH}{)}_6$
• Field-linear anomalous Hall effect and Berry curvature induced by spin chirality in the kagome antiferromagnet Mn3Sn
• Flat band separation and robust spin-Berry curvature in bilayer kagome metals
• Quantum computation with graphene nanoribbon
• Intrinsic spin Nernst effect of magnons in a noncollinear antiferromagnet
• Superconductivity and orbital-selective nematic order in a new titanium-based kagome metal CsTi3Bi5
• Quantum Interactions in Topological R166 Kagome Magnet
• Three-dimensional electronic structure in ferromagnetic ${\text{Fe}}_3{\text{Sn}}_2$ with breathing kagome bilayers
• Orbital Hall effect and orbital edge states caused by s electrons
• Anomalous Hall Effect due to the spin chirality in the Kagomé lattice
• Spin Hall effect in the kagome lattice with Rashba spin-orbit interaction
• Dynamical Study of the Origin of the Charge Density Wave in $A$V${}_3$Sb${}_5$ ($A=$K, Rb, Cs) Compounds
• Magnus Hall effect in three-dimensional topological semimetals
• Ferromagnetic helical nodal line and Kane-Mele spin-orbit coupling in kagome metal Fe3Sn2
• Spin density wave and van Hove singularity in the kagome metal CeTi3Bi4
• Realization of Kagome Kondo lattice
• Magnetic orderings from spin-orbit coupled electrons on kagome lattice
• Full analytical solution of finite-length armchair/zigzag nanoribbons
• Lattice-commensurate skyrmion texture in a centrosymmetric breathing kagome magnet
• Ground-state magnetic structures of topological kagome metals RV${}_6$Sn${}_6$ (R = Tb, Dy, Ho, Er)
• Canted Antiferromagnetic Order in the Kagome Material Sr-Vesignieite
• Perspective: imaging atomic step geometry to determine surface terminations of kagome materials and beyond
• Spin waves and orbital contribution to ferromagnetism in a topological metal
• Localization, transport and edge states in a two-strand ladder network in an aperiodically staggered magnetic field