论文标题
奇异的平坦乐队
Singular flat bands
论文作者
论文摘要
我们回顾了平面系统研究的最新进展，尤其是关注与平面频段Bloch波函数的奇异性有关的基本物理学。我们首先解释说，基于平面频段的Bloch波函数中的奇异性，可以将平面带分为两个类别：奇异和非词段。奇异性是由平面带与另一个色散频带的频段交叉产生的。在奇异的平坦频段中，人们可以找到一种特殊的本征谱，称为非摘除环状态和强大的边界模式，这些模式表现出非平凡的真实空间拓扑。然后，我们回顾了光子晶格中平面带的这些拓扑本征的实验实现。虽然平面频带的奇异性在拓扑上是微不足道的，但我们表明，奇异性周围的最大量子距离是代表奇异性强度的庞大不变性，可保护可靠的边界模式。最后，我们讨论了最大量子距离或奇异性的强度如何在与另一个频段进行二次频带横断时，在奇异平面频段的异常兰道水平上如何表现出来。
We review recent progresses in the study of flat band systems, especially focusing on the fundamental physics related to the singularity of the flat band's Bloch wave functions. We first explain that the flat bands can be classified into two classes: singular and nonsingular flat bands, based on the presence or absence of the singularity in the flat band's Bloch wave functions. The singularity is generated by the band crossing of the flat band with another dispersive band. In the singular flat band, one can find special kind of eigenmodes, called the non-contractible loop states and the robust boundary modes, which exhibit nontrivial real space topology. Then, we review the experimental realization of these topological eigenmodes of the flat band in the photonic lattices. While the singularity of the flat band is topologically trivial, we show that the maximum quantum distance around the singularity is a bulk invariant representing the strength of the singularity which protects the robust boundary modes. Finally, we discuss how the maximum quantum distance or the strength of the singularity manifests itself in the anomalous Landau level spreading of the singular flat band when it has a quadratic band-crossing with another band.
