Studies of moiré systems have explained the effect of superlattice modulations on their properties, demonstrating new correlated phases¹. However, most experimental studies have focused on a few layers in two-dimensional systems. Extending twistronics to three dimensions, in which the twist extends into the third dimension, remains underexplored because of the challenges associated with the manual stacking of layers. Here we study three-dimensional twistronics using a self-assembled twisted spiral superlattice of multilayered WS₂. Our findings show an opto-twistronic Hall effect driven by structural chirality and coherence length, modulated by the moiré potential of the spiral superlattice. This is an experimental manifestation of the noncommutative geometry of the system. We observe enhanced light–matter interactions and an altered dependence of the Hall coefficient on photon momentum. Our model suggests contributions from higher-order quantum geometric quantities to this observation, providing opportunities for designing quantum-materials-based optoelectronic lattices with large nonlinearities.

对莫尔系统的研究已经解释了超晶格调制对其特性的影响，证明了新的相关相¹。然而，大多数实验研究都集中在二维系统中的几层上。由于与手动堆叠层相关的挑战，将 twistronics 扩展到三维（其中扭曲延伸到三维）仍未得到充分探索。在这里，我们使用多层 WS₂ 的自组装扭曲螺旋超晶格研究三维扭曲。我们的研究结果表明，由结构手性和相干长度驱动的光旋霍尔效应，受螺旋超晶格的莫尔势调制。这是系统非交换几何的实验表现。我们观察到光-物质相互作用增强，霍尔系数对光子动量的依赖性发生了变化。我们的模型表明高阶量子几何量对这一观察结果有贡献，为设计具有大非线性的基于量子材料的光电晶格提供了机会。