Exploration of the impact of synthetic material landscapes featuring tunable geometrical properties on physical processes is a research direction that is currently of great interest because of the outstanding phenomena that are continually being uncovered. Twistronics and the properties of wave excitations in moiré lattices are salient examples. Moiré patterns bridge the gap between aperiodic structures and perfect crystals, thus opening the door to the exploration of effects accompanying the transition from commensurate to incommensurate phases. Moiré patterns have revealed profound effects in graphene-based systems^1,2,3,4,5, they are used to manipulate ultracold atoms^6,7 and to create gauge potentials⁸, and are observed in colloidal clusters⁹. Recently, it was shown that photonic moiré lattices enable observation of the two-dimensional localization-to-delocalization transition of light in purely linear systems^10,11. Here, we employ moiré lattices optically induced in photorefractive nonlinear media^12,13,14 to elucidate the formation of optical solitons under different geometrical conditions controlled by the twisting angle between the constitutive sublattices. We observe the formation of solitons in lattices that smoothly transition from fully periodic geometries to aperiodic ones, with threshold properties that are a pristine direct manifestation of flat-band physics¹¹.

探究具有可调整的几何特性的合成材料景观对物理过程的影响是一个研究方向，由于不断发现的杰出现象，当前该研究方向引起了人们的极大兴趣。Twistronics和摩尔纹格中的波激发特性是明显的例子。莫尔条纹弥合了非周期性结构与完美晶体之间的间隙，从而为探索从相称相向不相称相伴随的效应打开了大门。莫尔图案已揭示出在基于石墨烯的系统^{1,2,3,4,5中的}深刻影响，它们被用来操纵超冷原子^6,7并产生标称电势⁸，并在胶体簇中被观察到^9。。最近，显示出光子莫尔条纹使得能够观察纯线性系统^10,11中光的二维定位到离域转变。在这里，我们采用在光折射非线性介质^{12、13、14中}光学诱导的莫尔网格，以阐明在本构亚晶格之间的扭转角控制的不同几何条件下，光学孤子的形成。我们观察到晶格中孤子的形成，这些晶格从全周期几何平稳过渡到非周期几何，其阈值性质是平带物理学¹¹的原始直接体现。