论文标题
二维顶点装饰的LIEB晶格，具有精确的移动性边缘和稳健的平坦带
Two dimensional vertex-decorated Lieb lattice with exact mobility edges and robust flat bands
论文作者
论文摘要
标记能量分离扩展和局部状态的迁移率边缘（ME）是理解由无序或准碘电势引起的金属 - 绝缘体过渡的核心概念。 ME已在三维疾病系统和一维准膜系统中进行了广泛的研究。但是，在二维（2D）系统中对ME的研究很少见。在这里，我们提出了一类二维顶点装饰的Lieb晶格模型，其甲状腺素电位仅作用于（扩展）Lieb晶格的顶点。通过将这些模型映射到2D Aubry-André模型中，我们获得了MES的精确表达式和局部状态的定位长度，并进一步证明了平面带不受Quasiperiodic电位的影响。最后，我们提出了一个高度可行的方案，以实验在量子点阵列中实现我们的模型。我们的结果为在2D系统中研究和实现精确的MES和稳健的扁平频段打开了大门。
The mobility edge (ME) that marks the energy separating extended and localized states is a central concept in understanding the metal-insulator transition induced by disordered or quasiperiodic potentials. MEs have been extensively studied in three dimensional disorder systems and one-dimensional quasiperiodic systems. However, the studies of MEs in two dimensional (2D) systems are rare. Here we propose a class of 2D vertex-decorated Lieb lattice models with quasiperiodic potentials only acting on the vertices of a (extended) Lieb lattice. By mapping these models to the 2D Aubry-André model, we obtain exact expressions of MEs and the localization lengths of localized states, and further demonstrate that the flat bands remain unaffected by the quasiperiodic potentials. Finally, we propose a highly feasible scheme to experimentally realize our model in a quantum dot array. Our results open the door to studying and realizing exact MEs and robust flat bands in 2D systems.
