Isolated Flat Bands and Spin-1 Conical Bands in Two-Dimensional Lattices

Abstract

Dispersionless bands, such as Landau levels, serve as a good starting point for obtaining interesting correlated states when interactions are added. With this motivation in mind, we study a variety of dispersionless ("flat") band structures that arise in tight-binding Hamiltonians defined on hexagonal and kagome lattices with staggered fluxes. The flat bands and their neighboring dispersing bands have several notable features: (a) Flat bands can be isolated from other bands by breaking time reversal symmetry, allowing for an extensive degeneracy when these bands are partially filled; (b) An isolated flat band corresponds to a critical point between regimes where the band is electron-like or hole-like, with an anomalous Hall conductance that changes sign across the transition; (c) When the gap between a flat band and two neighboring bands closes, the system is described by a single spin-1 conical-like spectrum, extending to higher angular momentum the spin-1/2 Dirac-like spectra in topological insulators and graphene; and (d) some configurations of parameters admit two isolated parallel flat bands, raising the possibility of exotic "heavy excitons"; (e) We find that the Chern number of the flat bands, in all instances that we study here, is zero.

7 pages. Sec. II slightly expanded. References added

References in corpus (3)

• Flat bands and Wigner crystallization in the honeycomb optical lattice
• Massless Dirac-Weyl Fermions in a T_3 Optical Lattice
• The $p_{x,y}$-orbital counterpart of graphene: cold atoms in the honeycomb optical lattice

Cited by in corpus (111)

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• The Rare Two-Dimensional Materials with Dirac Cones
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• Flat bands in topological media
• Intrinsic Quantum Anomalous Hall Effect in the Kagome Lattice Cs2LiMn3F12
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• Bose condensation in flat bands
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• Fractional topological liquids with time-reversal symmetry and their lattice realization
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• Flat Bands Under Correlated Perturbations
• Lattice generalization of the Dirac equation to general spin and the role of the flat band
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• Chiral Flat Bands: Existence, Engineering and Stability
• Effective theory and emergent $SU(2)$ symmetry in the flat bands of attractive Hubbard models
• Topological phase transitions driven by next-nearest-neighbor hopping in two-dimensional lattices
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• Dirac-Weyl fermions with arbitrary spin in two-dimensional optical superlattices
• Topological phase transitions and chiral inelastic transport induced by the squeezing of light
• Many-Body Quantum Electrodynamics Networks: Non-Equilibrium Condensed Matter Physics with Light
• Topological Phases in InAs${}_{1-x}$Sb${}_x$: From Novel Topological Semimetal to Majorana Wire
• Massive symmetry breaking in LaAlO${}_3$/SrTiO${}_3$(111) quantum wells: a three-orbital, strongly correlated generalization of graphene
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• Electron states for gapped pseudospin-1 fermions in the field of charged impurity
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• Challenging Magnetic Field Dependence of the Residual Resistivity of the Heavy-Fermion Metal CeCoIn5
• Thermodynamic Properties of Kagome Lattice in ZnCu_3(OH)_6Cl_2 Herbertsmithite
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• Chern-Simons Composite Fermion Theory of Fractional Chern Insulators
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• Scaling in Dynamic Susceptibility of Herbertsmithite and Heavy-Fermion Metals
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• Fate of localization features in a one-dimensional non-Hermitian flat-band lattice with quasiperiodic modulations
• Discovering Strongly Correlated Quantum Spin Liquid
• Anomalous in-gap edge states in two-dimensional pseudospin-1 Dirac insulators
• Holographic Lieb lattice and gapping its Dirac band
• Fermion condensate generates a new state of matter by making flat bands
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• Boundary Flat Bands with Topological Spin Textures Protected by Sub-chiral Symmetry
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