Disorder effects in the two-dimensional Lieb lattice and its extensions

2020/01/31 by Xiaoyu Mao, Jie Liu, Jianxin Zhong +1 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Computer science #Condensed matter physics #Lattice (music) #Physics #Quantum Mechanics and Non-Hermitian Physics #Statistical physics #Topological Materials and Phenomena #cond-mat.dis-nn #cond-mat.str-el

paper · pdf · doi:10.1016/j.physe.2020.114340

published as Phys. E Low-Dimensional Syst. Nanostructures 124, 114340 (2020) · 7 pages, 20 figures, 1 table

arxiv created 2020/07/02 · openalex publication_date 2020/07/09 · arxiv updated 2020/08/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We study the localization properties of the two-dimensional Lieb lattice and its extensions in the presence of disorder using transfer matrix method and finite-size scaling. We find that all states in the Lieb lattice and its extensions are localized for W ≥ 1. Clear differences in the localization properties between disordered flat band and disordered dispersive bands are identified. Our results complement previous experimental studies of clean photonic Lieb lattices and provide information about their stability with respect to disorder.

Citations

• The renormalization group and the ε expansion
• Disorder and interactions in Aharonov-Bohm cages
• Flat Bands and Wigner Crystallization in the Honeycomb Optical Lattice
• Weak-disorder expansion for localization lengths of quasi-1D systems
• Numerical studies of localization in disordered systems
• Random-matrix theory of quantum transport

Cited by

• Quantum-gas microscopy of the Bose-glass phase