Related papers: Two dimensional vertex-decorated Lieb lattice with exact mobility edges and robust flat bands

Two dimensional vertex-decorated Lieb lattice with exact mobility edges and robust flat bands

URL: http://arxiv.org/abs/2209.14741v4
Date: Mon, 24 Apr 2023 03:32:56 GMT
Title: Two dimensional vertex-decorated Lieb lattice with exact mobility edges and robust flat bands
Authors: Yucheng Wang, Long Zhang, Yuhao Wan, Yu He, and Yongjian Wang
Abstract summary: 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. Here we propose a class of 2D-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-Andr'e 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.
Score: 7.4705069914791045
License: http://creativecommons.org/licenses/by/4.0/
Abstract: 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-Andr\'{e} 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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