We show how the index of the fermion operator from the Euclidean action can be used to uncover the existence of gapless modes living on defects (such as edges and vortices) in topological insulators and superconductors. The 1-loop Feynman diagram that computes the index reveals an analog of the quantum Hall current flowing on and off the defect—even in systems without conserved currents or chiral anomalies—and makes explicit the interplay between topology in momentum and coordinate space. We provide several explicit examples.

中文翻译：

---

无间隙缺陷费米子的指数定理、广义霍尔电流和拓扑

我们展示了如何使用来自欧几里德作用的费米子算子的指数来揭示存在于拓扑绝缘体和超导体中的缺陷（例如边缘和涡旋）上的无间隙模式的存在。计算指数的 1 环费曼图揭示了在缺陷上流动和流出的量子霍尔电流的模拟——即使在没有守恒电流或手性异常的系统中也是如此——并明确了动量和坐标空间中的拓扑结构之间的相互作用。我们提供了几个明确的例子。