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

TL;DR

This paper investigates flat and spin-1 conical bands in 2D lattices, revealing their topological properties, degeneracies, and potential for exotic excitations, with implications for correlated states and topological phases.

Contribution

It introduces new flat band and spin-1 conical band structures in hexagonal and kagome lattices with staggered fluxes, highlighting their topological and degeneracy features.

Findings

Flat bands can be isolated by breaking time reversal symmetry.

An isolated flat band acts as a critical point with sign-changing Hall conductance.

Closing the gap leads to a spin-1 conical spectrum.

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.