论文标题
勇士格拉维斯的瓦尼尔 - 史塔布尔带
Wannier-Stark flatbands in Bravais lattices
论文作者
论文摘要
我们系统地构造了在静态统一DC字段的情况下，在空间尺寸的简单Bravais晶格上构建平面模型$ D \ GEQ 2 $。相应的直流场指示在垂直尺寸$ d-1 $带有$ d $维二维的特征函数中产生不可约的Wannier-Stark（WS）乐队。在没有垂直于直流场的任何方向上的晶格站点之间没有最近的邻居跳跃的情况下，不可约束的带变成了无散的平带。产生平板带的相称方向的数量是量度之一。我们到达了完全停止的运输，DC场禁止沿田间方向运输，并且在所有垂直方向上也禁止运输。各向异性平板特征态至少在分数上定位（比指数快）。
We systematically construct flatbands (FB) for tight-binding models on simple Bravais lattices in space dimension $d \geq 2$ in the presence of a static uniform DC field. Commensurate DC field directions yield irreducible Wannier-Stark (WS) bands in perpendicular dimension $d - 1$ with $d$-dimensional eigenfunctions. The irreducible bands turn into dispersionless flatbands in the absence of nearest neighbor hoppings between lattice sites in any direction perpendicular to the DC field. The number of commensurate directions which yield flatbands is of measure one. We arrive at a complete halt of transport, with the DC field prohibiting transport along the field direction, and the flatbands prohibiting transport in all perpendicular directions as well. The anisotropic flatband eigenstates are localizing at least factorially (faster than exponential).
