Higher-Order Van Hove Singularities in Kagome Topological Bands

Abstract

Motivated by the growing interest in band structures featuring higher-order Van Hove singularities (HOVHS), we investigate a spinless fermion kagome system characterized by nearest-neighbor (NN) and next-nearest-neighbor (NNN) hopping amplitudes. While NN hopping preserves time-reversal symmetry, NNN hopping, akin to chiral hopping on the Haldane lattice, breaks time-reversal symmetry and leads to the formation of topological bands with Chern numbers ranging from $C=\pm 1$ to $\pm 4$. We perform analytical and numerical analysis of the energy bands near the high-symmetry points $\mathbf{\Gamma }$, $\pm \mathbf{K}$, and ${\mathbf{M}}_{\mathbf{i}}$ ($i=1,2,$ and $3$), which uncover a rich and complex landscape of HOVHS, controlled by the magnitude and phase of the NNN hopping. We observe power-law divergences in the density of states (DOS), $\rho (\epsilon )\sim |\epsilon {|}^{-\nu }$, with exponents $\nu =1/2,1/3,1/4$, which can significantly affect the anomalous Hall response at low temperatures when the Fermi level crosses the HOVHS. Additionally, the NNN hopping induces the formation of higher Chern number bands $C=\pm 2,\pm 4$ in the middle of the spectrum obeying a sublattice interference whereupon electronic states are maximally localized in each of the sublattices when the momentum approaches the three high-symmetry points ${\mathbf{M}}_{\mathbf{i}}$ ($i=1,2,$ and $3$) on the Brillouin zone boundary. This classification of HOVHS in kagome systems provides a platform to explore unconventional electronic orders induced by electronic correlations.

11 pages, 7 figures

References in corpus (27)

• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• CsV${}_3$Sb${}_5$: a ${\mathbb{Z}}_2$ topological kagome metal with a superconducting ground state
• Nearly-flat bands with nontrivial topology
• Fractional quantum Hall effect in the absence of Landau levels
• Flat bands and Wigner crystallization in the honeycomb optical lattice
• Topological kagome magnets and superconductors
• Unconventional Fermi surface instabilities in the Kagome Hubbard Model
• Three-dimensional charge density wave and robust zero-bias conductance peak inside the superconducting vortex core of a kagome superconductor CsV${}_3$Sb${}_5$
• Discovery of charge density wave in a correlated kagome lattice antiferromagnet
• Nature of unconventional pairing in the kagome superconductors AV${}_3$Sb${}_5$
• Rotation symmetry breaking in the normal state of a kagome superconductor KV3Sb5
• Rich Nature of Van Hove Singularities in Kagome Superconductor CsV${}_3$Sb${}_5$
• Kagome superconductors AV${}_3$Sb${}_5$ (A=K, Rb, Cs)
• Complex charge density waves at Van Hove singularity on hexagonal lattices: Haldane-model phase diagram and potential realization in kagome metals ${\text{AV}}_3{\text{Sb}}_5$
• Interaction-driven topological insulators on the kagome and the decorated honeycomb lattices
• Intertwined magnetism and charge density wave order in kagome FeGe
• Discovery of charge order and corresponding edge state in kagome magnet FeGe
• Charge order landscape and competition with superconductivity in kagome metals
• Competing orders at higher-order Van Hove points
• Chiral excitonic order from twofold van Hove singularities in kagome metals
• Pair-density-wave and chiral superconductivity in twisted bilayer transition-metal-dichalcogenides
• Spin-valley locked instabilities in moire transition metal dichalcogenides with conventional and higher-order Van Hove singularities
• Emergence of Chern Supermetal and Pair-Density Wave through Higher-Order Van Hove Singularities in the Haldane-Hubbard Model
• Van-Hove annihilation and nematic instability on a Kagome lattice
• Sublattice modulated superconductivity in the Kagome Hubbard model
• Single monkey-saddle singularity of a Fermi surface and its instabilities

Cited by in corpus (2)

• Designing Topological High-Order Van Hove Singularities: Twisted Bilayer Kagomé
• Kekulé order from diffuse nesting near higher-order Van Hove points