Non-perturbative dynamics of flat-band systems with correlated disorder

doi:10.1088/1674-1056/ad5534

Abstract We develop a numerical method for the time evolution of Gaussian wave packets on flat-band lattices in the presence of correlated disorder. To achieve this, we introduce a method to generate random on-site energies with prescribed correlations. We verify this method with a one-dimensional (1D) cross-stitch model, and find good agreement with analytical results obtained from the disorder-dressed evolution equations. This allows us to reproduce previous findings, that disorder can mobilize 1D flat-band states which would otherwise remain localized. As explained by the corresponding disorder-dressed evolution equations, such mobilization requires an asymmetric disorder-induced coupling to dispersive bands, a condition that is generically not fulfilled when the flat-band is resonant with the dispersive bands at a Dirac point-like crossing. We exemplify this with the 1D Lieb lattice. While analytical expressions are not available for the two-dimensional (2D) system due to its complexity, we extend the numerical method to the 2D $\alpha$-$T_3$ model, and find that the initial flat-band wave packet preserves its localization when $\alpha = 0$, regardless of disorder and intersections. However, when $\alpha\neq 0$, the wave packet shifts in real space. We interpret this as a Berry phase controlled, disorder-induced wave-packet mobilization. In addition, we present density functional theory calculations of candidate materials, specifically ${\rm Hg}_{1-x}{\rm Cd}_x{\rm Te}$. The flat-band emerges near the $\varGamma$ point (${\bm k}=0$) in the Brillouin zone.

Keywords: flat-band system dynamics correlated disorder

Received: 12 February 2024
Revised: 24 May 2024
Accepted manuscript online: 07 June 2024

PACS:	72.80.Ng	(Disordered solids)
	78.20.Bh	(Theory, models, and numerical simulation)
	67.80.de	(Structure, lattice dynamics and sound)
	05.50.+q	(Lattice theory and statistics)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 61988102), the Key Research and Development Program of Guangdong Province (Grant No. 2019B090917007), and the Science and Technology Planning Project of Guangdong Province (Grant No. 2019B090909011). Q. L. acknowledges Guangzhou Basic and Applied Basic Research Project (Grant No. 2023A04J0018). Z. L. acknowledges the support of funding from Chinese Academy of Sciences E1Z1D10200 and E2Z2D10200; from ZJ project 2021QN02X159 and from JSPS (Grant Nos. PE14052 and P16027). We gratefully acknowledge HZWTECH for providing computation facilities. Z.-X. H. was supported by the National Natural Science Foundation of China (Grant Nos. 11974064 and 12147102) and the Fundamental Research Funds for the Central Universities (Grant No. 2020CDJQY-Z003).

Corresponding Authors: Zhou Li
E-mail: liz@aircas.ac.cn

Cite this article:

Qi Li(李骐), Junfeng Liu(刘军丰), Ke Liu(刘克), Zi-Xiang Hu(胡自翔), and Zhou Li(李舟) Non-perturbative dynamics of flat-band systems with correlated disorder 2024 Chin. Phys. B 33 097203

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Non-perturbative dynamics of flat-band systems with correlated disorder

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