Topological Aspects of Dirac Fermions in a Kagomé Lattice

Abstract

The Dirac fermion with linear dispersion in the kagomé lattice governs the low-energy physics of different valleys at two inequivalent corners of hexagonal Brillouin zone. The effective Hamiltonian based on the cyclic permutation symmetry of sublattices is constructed to show that the topology of Dirac fermions at these two valleys is characterized by opposite winding numbers. For spinless fermions, the many-particle interactions produce intervalley scattering and drive an intervalley coherent state with spontaneous translation symmetry breaking. The Dirac fermions acquire a mass term from the simultaneous charge and bond orderings. In this phase, the developed bond texture underlies a hollow-star-of-David pattern in a tripled Wigner-Seitz cell of kagomé lattice. It is further demonstrated that the twisting of Dirac mass with vorticity leads to zero Dirac modes at the vortex core, which are intimately related to fractionalization. The hollow-star-of-David phase is shown to have a distinct ${\mathbb{Z}}_6$ Berry phase with its sign-change counterpart of Dirac mass, i.e. the hexagonal phase, shedding light on the topological origin of zero Dirac modes around the vortex core.

arXiv comment8 pages, 4 figures

References in corpus (68)

• Many-Body Physics with Ultracold Gases
• Quantum Spin Hall Effect in Graphene
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Quantized Electric Multipole Insulators
• Higher-Order Topological Insulators
• 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
• Massive Dirac fermions in a ferromagnetic kagome metal
• Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices
• Acoustic higher-order topological insulator on a Kagome lattice
• Discovery of unconventional chiral charge order in kagome superconductor KV3Sb5
• Dirac fermions and flat bands in the ideal kagome metal FeSn
• Topological insulator on the kagome lattice
• Discovery of a quantum limit Chern magnet TbMn6Sn6
• Topological kagome magnets and superconductors
• Unconventional Fermi surface instabilities in the Kagome Hubbard Model
• Charge density waves and electronic properties of superconducting kagome metals
• Electron fractionalization in two-dimensional graphenelike structures
• Competing electronic orders on Kagome lattices at van Hove filling
• Ultracold Atoms in a Tunable Optical Kagome Lattice
• Magnetic confinement of massless Dirac fermions in graphene
• Corner states of light in photonic waveguides
• Topological flat bands in frustrated kagome lattice CoSn
• Strong coupling phases of partially filled twisted bilayer graphene narrow bands
• Chiral flux phase in the Kagome superconductor AV${}_3$Sb${}_5$
• Discovery of charge density wave in a correlated kagome lattice antiferromagnet
• Ground State and Hidden Symmetry of Magic Angle Graphene at Even Integer Filling
• Correlation-driven chiral superconductivity and chiral spin order in doped kagome lattice
• Sublattice Interference in the Kagome Hubbard Model
• Nature of unconventional pairing in the kagome superconductors AV${}_3$Sb${}_5$
• Intrinsic Quantum Anomalous Hall Effect in the Kagome Lattice Cs2LiMn3F12
• Rich Nature of Van Hove Singularities in Kagome Superconductor CsV${}_3$Sb${}_5$
• Robust zero-energy modes in an electronic higher-order topological insulator: the dimerized Kagome lattice
• Interaction-driven topological insulators on the kagome and the decorated honeycomb lattices
• Orbital-selective Dirac fermions and extremely flat bands in frustrated kagome-lattice metal CoSn
• Ferromagnetic Mott State in Twisted Graphene Bilayers at the Magic Angle
• Charge density wave in kagome lattice intermetallic ScV6Sn6
• Chiral Gauge Theory for Graphene
• Quantum states and intertwining phases in kagome materials
• Twisted bilayer graphene III. Interacting Hamiltonian and exact symmetries
• Observation of topological flat bands in the kagome semiconductor Nb${}_3$Cl${}_8$
• Charge-order-assisted topological surface states and flat bands in the kagome superconductor CsV${}_3$Sb${}_5$
• Topological states on the breathing kagome lattice
• Realizing Kagome Band Structure in Two-Dimensional Kagome Surface States of $R{V}_{6}S{n}_6$ ($R$=Gd,Ho)
• Tunable Topological Dirac Surface States and Van Hove Singularities in Kagome Metal GdV${}_6$Sn${}_6$
• Majorana-like zero modes in Kekulé distorted sonic lattices
• Electron fractionalization for two-dimensional Dirac fermions
• $Z_Q$ Topological Invariants for Polyacetylene, Kagome and Pyrochlore lattices
• Interaction-Driven Spontaneous Quantum Hall Effect on Kagome Lattice
• Strongly correlated fermions on a kagome lattice
• Fractionally charged topological point defects on the kagome lattice
• Optical spectroscopy and band structure calculations of structural phase transition in the Vanadium-based kagome metal ScV${}_6$Sn${}_6$
• Spectroscopic evidence of flat bands in breathing kagome semiconductor Nb3I8
• A Photonic Topological Mode Bound to a Vortex
• Discovery of a Single-Band Mott Insulator in a van der Waals Flat-Band Compound
• Loop-current charge density wave driven by long-range Coulomb repulsion on the kagome lattice
• Spontaneous symmetry breakings in two-dimensional kagome lattice
• First and Second Order Topological Phases on Ferromagnetic Breathing Kagome Lattice
• Corner modes of the breathing kagome lattice: origin and robustness
• Fractional statistics of topological defects in graphene and related structures
• Tunning topological phase and quantum anomalous Hall effect by interaction in quadratic band touching systems
• Phase diagram of the 1/3-filled extended Hubbard model on the Kagome lattice
• Observation of Kekulé vortices induced in graphene by hydrogen adatoms
• Quantum Anomalous Hall Phase Stabilized via Realistic Interactions on a Kagome Lattice
• Flow-Induced Charge Modulation in Superfluid Atomic Fermions Loaded into an Optical Kagome Lattice
• Charge bond order and s-wave superconductivity in the kagome lattice with electron-phonon coupling and electron-electron interaction