We show that weak measurements can be used to measure the tiny signature of topological phase transitions. The signature is an in-plane photonic spin Hall effect, which can be described as a consequence of a Berry phase. It is also parallel to the propagation direction of a light beam. The imaginary part of the weak value can be used to analyze ultrasmall longitudinal phase shifts in different topological phases. These optical signatures are related to the Chern number and bandgaps; we also use a preselection and postselection technique on the spin state to enhance the original signature. The weak amplification technique offers a potential way to determine the spin and valley properties of charge carriers, Chern numbers, and topological phases by direct optical measurement.

中文翻译：

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拓扑相变光学特征的弱值放大

我们表明弱测量可用于测量拓扑相变的微小特征。特征是面内光子自旋霍尔效应，可以将其描述为 Berry 相的结果。它也平行于光束的传播方向。弱值的虚部可用于分析不同拓扑相中的超小纵向相移。这些光学特征与陈数和带隙有关；我们还在自旋状态上使用预选和后选技术来增强原始签名。弱放大技术提供了一种通过直接光学测量来确定电荷载流子、陈数和拓扑相的自旋和谷特性的潜在方法。