We study the localization properties of the two-dimensional Lieb lattice and its extensions in the presence of disorder using the transfer matrix method and finite-size scaling. We find that all states in the Lieb lattice and its extensions are localized for $W\ge 1$. Clear differences in the localization properties between disordered flat bands 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.

中文翻译：

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二维Lieb晶格及其扩展中的无序效应

我们使用转移矩阵方法和有限尺寸缩放研究二维Lieb晶格的局部化特性及其在无序情况下的扩展。我们发现，李卜网格中的所有状态及其扩展都被局部化为 $\mathrm{w\; ^}\ge \mathrm{1个}$。鉴定出无序平坦带和无序分散带之间的定位特性存在明显差异。我们的结果补充了先前对清洁光子利勃晶体的实验研究，并提供了有关无序稳定性的信息。