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arXiv · 2305.18759

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

Qi Li·Junfeng Liu·Ke Liu·Zi-Xiang Hu·Zhou Li
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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 $α-T_3$ model, and find that the initial flat-band wave packet preserves its localization when $α= 0$, regardless of disorder and intersections. However, when $α\neq 0$, 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 $Γ$ point ($\bf{k}=$0) in the Brillouin zone.

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Qi Li, Junfeng Liu, Ke Liu, Zi-Xiang Hu, Zhou Li. 2024-06-21. Non-perturbative dynamics of flat-band systems with correlated disorder. https://doi.org/10.1088/1674-1056%2Fad5534

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