When electrons are confined to a two-dimensional plane and are subjected to an out-of-plane magnetic field, they move in circular cyclotron orbits as a result of the Lorentz force. In the quantum domain, this cyclotron motion is quantized, and as a consequence, the energy spectrum of the electrons splits into discrete, highly degenerate states called Landau levels. These flat bands are the origin of the integer and fractional quantum Hall effects^1,2. Although photons do not experience the Lorentz force because they do not carry charge, they can be made to experience ‘pseudomagnetic fields’^3,4 as a result of periodicity-breaking strain. In this work, we experimentally observe photonic Landau levels that arise due to a strain-induced pseudomagnetic field in a silicon photonic crystal slab. The Landau levels are dispersive (that is, they are not flat bands) due to the distortion of the unit cell by the strain. We employ an additional strain of a different form that induces a pseudoelectric potential to flatten them. By acting akin to cavities that are delocalized across space, flat bands such as these have the potential to strongly enhance light–matter interaction as a result of the photonic structure. The analytical framework that we develop here for understanding the effects of inhomogeneous strain in photonic crystals via gauge fields can help to guide the design of multiscale non-periodic photonic structures.

当电子被限制在二维平面内并受到平面外磁场时，它们由于洛伦兹力而在圆形回旋轨道上移动。在量子域中，这种回旋运动被量子化，因此，电子的能谱分裂成离散的、高度简并的状态，称为朗道能级。这些平带是整数和分数量子霍尔效应的起源^1,2。尽管光子因为不携带电荷而不会受到洛伦兹力，但由于周期性破坏应变，它们可以受到“赝磁场” ^3,4 。在这项工作中，我们通过实验观察了硅光子晶体板中因应变感应赝磁场而产生的光子朗道能级。由于应变导致晶胞变形，朗道能级是色散的（即，它们不是平带）。我们采用不同形式的额外应变来感应赝电势以压平它们。通过类似于跨空间离域的空腔，诸如此类的平带有可能由于光子结构而强烈增强光与物质的相互作用。我们在这里开发的用于通过规范场了解光子晶体中不均匀应变的影响的分析框架可以帮助指导多尺度非周期光子结构的设计。