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  • Letter

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

Yucheng Wang1,2,3,*, Long Zhang4, Yuhao Wan5, Yu He1,2,3,†, and Yongjian Wang6,‡

  • 1Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
  • 2International Quantum Academy, Shenzhen 518048, China
  • 3Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
  • 4School of Physics and Institute for Quantum Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
  • 5International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
  • 6School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, MOE, Beijing Normal University, Beijing 100875, China

  • *Corresponding author: wangyc3@sustech.edu.cn
  • †Corresponding author: hey6@sustech.edu.cn
  • ‡Corresponding author: wangyongjian@amss.ac.cn
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Phys. Rev. B 107, L140201 – Published 17 April, 2023

DOI: https://doi.org/10.1103/PhysRevB.107.L140201

Abstract

The mobility edge (ME) that marks the energy separating extended and localized states is a most important 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 the Lieb lattice or extended Lieb lattices. 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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Phys. Rev. B 107, L140201– Published 17 April, 2023
  • Received 3 October 2022
  • Accepted 11 April 2023
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