二维晶格中孤立的平带和自旋为1的锥形带
Isolated Flat Bands and Spin-1 Conical Bands in Two-Dimensional Lattices
摘要：
无色散带，如朗道能级，作为一个很好的起点，获得有趣的相关态时，相互作用。考虑到这一动机，我们研究了各种各样的色散（“平”）能带结构，出现在紧束缚哈密顿定义的六角形和kagome晶格交错通量。平带及其邻近的色散带具有几个显著的特征：（a）平带可以通过打破时间反演对称性而与其他带隔离，当这些带被部分填充时，允许广泛的简并;（b）隔离的平带对应于带是类电子或类空穴的状态之间的临界点，具有在过渡期间改变符号的异常霍尔电导;（c）当平带和两个相邻带之间的带隙闭合时，系统由单个自旋1类圆锥光谱描述，将拓扑绝缘体和石墨烯中的自旋1/2类狄拉克光谱扩展到更高的角动量;（d）某些参数配置允许两个孤立的平行平带，提高了奇异“重激子”的可能性;（e）我们发现，在我们这里研究的所有情况下，平坦带的Chern数都是零。
英文摘要：
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.
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