When quasiparticles move in condensed matters, the texture of their internal quantum structure as a function of position and momentum can give rise to Berry phases that have profound effects on the material’s properties. Seminal examples include the anomalous Hall and spin Hall effects from the momentum-space Berry phases in homogeneous crystals. Here, we explore a conjugate form of the electron Berry phase arising from the moiré pattern: the texture of atomic configurations in real space. In homobilayer transition metal dichalcogenides, we show that the real-space Berry phase from moiré patterns manifests as a periodic magnetic field with magnitudes of up to hundreds of Tesla. This quantity distinguishes moiré patterns from different origins, which can have an identical potential landscape, but opposite quantized magnetic flux per supercell. For low-energy carriers, the homobilayer moirés realize topological flux lattices for the quantum-spin Hall effect. An interlayer bias can continuously tune the spatial profile of the moiré magnetic field, whereas the flux per supercell is a topological quantity that can only have a quantized jump observable at a moderate bias. We also reveal the important role of the non-Abelian Berry phase in shaping the energy landscape in small moiré patterns. Our work points to new possibilities to access ultra-high magnetic fields that can be tailored to the nanoscale by electrical and mechanical controls.

中文翻译：

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同双层半导体中莫尔条纹引起的贝里相产生的巨大磁场


当准粒子在凝聚态物质中运动时，其内部量子结构的纹理作为位置和动量的函数会产生贝里相，这对材料的性质产生深远的影响。开创性的例子包括均质晶体中动量空间贝里相的反常霍尔效应和自旋霍尔效应。在这里，我们探索了由莫尔图案产生的电子贝里相的共轭形式：真实空间中原子构型的纹理。在同双层过渡金属二硫化物中，我们发现莫尔图案中的真实空间贝里相表现为强度高达数百特斯拉的周期性磁场。这个量区分了不同来源的莫尔图案，这些图案可以具有相同的潜在景观，但每个超级单元具有相反的量化磁通量。对于低能载流子，同双层莫尔条纹实现了量子自旋霍尔效应的拓扑通量晶格。层间偏置可以连续调节莫尔磁场的空间轮廓，而每个超晶胞的通量是一个拓扑量，只能在中等偏置下具有可观察到的量子化跳跃。我们还揭示了非阿贝尔贝里相在塑造小莫尔图案能量景观中的重要作用。我们的工作指出了获得超高磁场的新可能性，可以通过电气和机械控制将其定制为纳米级。