We investigate the electronic structure and the optical absorption onset of close-to-${30}^{\circ }$ twisted hexagonal boron nitride bilayers. Our study is carried out with a purposely developed tight-binding model validated against density functional theory simulations. We demonstrate that approaching ${30}^{\circ }$ (quasicrystal limit), all bilayers sharing the same moiré supercell develop identical band structures, irrespective of their stacking sequence. This band structure features a bundle of flat bands lying slightly above the bottom conduction state which is responsible for an intense peak at the onset of the absorption spectrum. These results suggest the presence of strong, stable and stacking-independent excitons in boron nitride ${30}^{\circ }$-twisted bilayers. By carefully analyzing the electronic structure and its spatial distribution, we elucidate the origin of these states as moiré-induced $K$-valley scattering due to interlayer $\mathrm{B}\text{−}\mathrm{B}$ coupling. We take advantage of the physical transparency of the tight-binding parameters to derive a simple triangular model based on the B sublattice that accurately describes the emergence of the bundle. As our conclusions very general, we predict that a similar bundle should emerge in other close-to-${30}^{\circ }$ bilayers, such as transition metal dichalcogenides, shedding light on the unique potential of two-dimensional materials.

中文翻译：

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氮化硼扭曲双层准晶极限中平带的出现

我们研究了接近的电子结构和光学吸收起始${30}^{\circ }$扭曲的六方氮化硼双层。我们的研究是使用专门开发的紧束缚模型进行的，该模型经过密度泛函理论模拟的验证。我们证明了接近${30}^{\circ }$（准晶体极限），共享相同莫尔超晶胞的所有双层都会形成相同的能带结构，无论其堆叠顺序如何。这种能带结构的特点是有一束平带，略高于底部传导态，这导致吸收光谱开始时出现强烈的峰值。这些结果表明氮化硼中存在强、稳定且与堆积无关的激子${30}^{\circ }$-扭曲双层。通过仔细分析电子结构及其空间分布，我们阐明了这些状态的起源为莫尔条纹引起的$K$- 由于夹层而产生的谷散射$\mathrm{乙}\text{-}\mathrm{乙}$耦合。我们利用紧束缚参数的物理透明性，导出了一个基于 B 子格的简单三角形模型，该模型准确地描述了束的出现。由于我们的结论非常笼统，我们预测类似的捆绑包应该出现在其他接近的地方${30}^{\circ }$双层，例如过渡金属二硫属化物，揭示了二维材料的独特潜力。