论文标题
拓扑绝缘体和超导体中的广义霍尔电流
Generalized Hall currents in topological insulators and superconductors
论文作者
论文摘要
我们将量化的霍尔电流的概念概括为在拓扑材料中计算无间隙边缘状态，同样适用于不同维度的理论，在边界上的散装或手性异常中，有或没有连续的对称性。该电流与欧几里得费米算子的索引有关，可以通过一环Feynman图来计算。电流的量化显示为相位空间中的拓扑控制，并且该过程可以应用于由$ {\ mathbb z} $或$ {\ Mathbb z} _2 $ noffariants支配的拓扑类别。我们分析了相对论领域理论中的几个明确示例。我们推测，也可以将技术扩展到相互作用的理论，例如相互作用差距在边缘状态的有趣情况。
We generalize the idea of the quantized Hall current to count gapless edge states in topological materials, applying equally well to theories in different dimensions, with or without continuous symmetries in the bulk or chiral anomalies on the boundaries. This current is related to the index of the Euclidean fermion operator and can be calculated via one-loop Feynman diagrams. Quantization of the current is shown to be governed by topology in phase space, and the procedure can be applied to topological classes governed by either ${\mathbb Z}$ or ${\mathbb Z}_2$ invariants. We analyze several explicit examples of free fermions in relativistic field theories. We speculate that it may be possible to extend the technique to interacting theories as well, such as the interesting cases where interactions gap the edge states.
