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

• URL: http://arxiv.org/abs/2305.18759v2
• Date: Fri, 21 Jun 2024 09:23:11 GMT
• Title: Non-perturbative dynamics of flat-band systems with correlated disorder
• Authors: Qi Li, Junfeng Liu, Ke Liu, Zi-Xiang Hu, Zhou Li,
• Abstract summary: We develop a numerical method for the time evolution of Gaussian wave packets on flat-band lattices in the presence of correlated disorder. We verify this method with a one-dimensional (1D) cross-stitch model. We find that disorder can mobilize 1D flat-band states which would otherwise remain localized.
• Score: 12.580323133885933
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $\rm Hg_{1-x}Cd_xTe$. The flat-band emerges near the $\Gamma$ point ($\bf{k}=$0) in the Brillouin zone.

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