The crystal structure of a material creates a periodic potential that electrons move through giving rise to its electronic band structure. When two-dimensional materials are stacked, the resulting moiré pattern introduces an additional periodicity so that the twist angle between the layers becomes an extra degree of freedom for the resulting heterostructure. As this angle changes, the electronic band structure is modified leading to the possibility of flat bands with localized states and enhanced electronic correlations^1,2,3,4,5,6. In transition metal dichalcogenides, flat bands have been theoretically predicted to occur for long moiré wavelengths over a range of twist angles around 0° and 60° (ref. ⁴) giving much wider versatility than magic-angle twisted bilayer graphene. Here, we show the existence of a flat band in the electronic structure of 3° and 57.5° twisted bilayer WSe₂ samples using scanning tunnelling spectroscopy. Our direct spatial mapping of wavefunctions at the flat-band energy show that the localization of the flat bands is different for 3° and 57.5°, in agreement with first-principles density functional theory calculations⁴.

材料的晶体结构会产生周期性的电势，电子会移动通过它，从而产生其电子能带结构。当堆叠二维材料时，所得的莫尔图案会引入额外的周期性，从而各层之间的扭曲角将成为所得异质结构的额外自由度。随着该角度的变化，电子带的结构被修改，导致具有局部状态的平坦带以及增强的电子相关性^1,2,3,4,5,6的可能性。在过渡金属二卤化物中，理论上已预测，在约0°和60°的扭曲角范围内，长莫尔波长会出现平坦带（参考文献^4）。）比魔角扭曲的双层石墨烯具有更大的通用性。在这里，我们使用扫描隧道光谱法显示了3°和57.5°扭曲双层WSe ₂样品的电子结构中存在平坦带。我们在平坦带能量处对波函数的直接空间映射表明，与第一原理密度泛函理论计算⁴一致，平坦带的局域性在3°和57.5°处不同。