具有精确迁移率边和鲁棒平带的二维顶点装饰Lieb晶格
Two dimensional vertex-decorated Lieb lattice with exact mobility edges and robust flat bands
AI总结：
针对二维系统中精确迁移率边研究不足的问题，提出准周期势仅作用于顶点的二维顶点装饰Lieb晶格模型，通过映射至二维Aubry-André模型导出精确迁移率边与局域化长度，并证明平带鲁棒且给出量子点阵列实现方案。
摘要：
标志着区分扩展态与局域态能量的迁移率边（ME），是理解由无序或准周期势诱导的金属-绝缘体转变的核心概念。ME已在三维无序系统和一维准周期系统中得到广泛研究。然而，二维（2D）系统中ME的研究仍较为稀少。本文提出一类二维顶点装饰Lieb晶格模型，其中准周期势仅作用于（扩展）Lieb晶格的顶点。通过将这些模型映射到二维Aubry-André模型，我们得到了ME的精确表达式以及局域态的局域化长度，并进一步证明平带不受准周期势影响。最后，我们提出一种在量子点阵列中实验实现该模型的高度可行方案。我们的结果为在二维系统中研究并实现精确ME和鲁棒平带打开了大门。
英文摘要：
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.
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