论文标题
分支机构中的平坦条带，边缘状态和可能的拓扑阶段
Flat bands, edge states and possible topological phases in a branching fractal
论文作者
论文摘要
我们解决了分析中提取较高和更高世代的分支vicsek几何形状的周期性阵列中平坦的非分散带的可数无穷大的问题。通过几何结构，随后是一个精确的真实空间重新归一化方案，我们揭开了紧凑的局部状态簇，对应于密集的平坦带的群，有时与分散型群体紧邻，因为单位细胞可容纳较高和上世代的Vicsek分形基序。在这样的周期性阵列中，能量频段以可以准确计算的能量封闭和开放，并且可以确定描述紧密结合系统的重叠积分之间的精确相关性。拓扑相变的可能性是通过对边缘状态的明确构造来指出的，受到弱保护，尽管有人认为在这种情况下，典型的散装 - 边界对应关系并不能保持良好。
We address the problem of analytically extracting a countable infinity of flat, non-dispersive bands in a periodic array of cells that comprise branching Vicsek geometries of higher and higher generations. Through a geometric construction, followed by an exact real space renormalization scheme we unravel clusters of compact localized states, corresponding to densely packed groups of flat bands, sometimes in close proximity with the dispersive ones, as the unit cells accommodate Vicsek fractal motifs of higher and higher generations. In such periodic arrays, energy bands close and open at energies that can be calculated exactly, and the precise correlation between the overlap integrals describing the tight binding systems can be worked out. The possibility of a topological phase transition is pointed out through an explicit construction of the edge states, weakly protected against disorder, though it is argued that the typical bulk-boundary correspondence is not holding good in such cases.
