论文标题
受C2T保护及其K理论不变性和材料实现的轴突绝缘子
Axion insulators protected by C2T and their K-theory invariants and material realization
论文作者
论文摘要
轴突绝缘子通常被理解为磁性拓扑绝缘子，其Chern-Simons Axion耦合项被量化，等于$π$。反转和时间逆转，或一个带有旋转或翻译的人的组成是保护这种不变的对称性。在这项工作中，我们将注意力集中在随时间逆转的2倍旋转的组成上，我们表明具有这种对称性的绝缘子具有由Atiyah的真实K理论引起的Z2不变性。由于与凯恩 - 梅勒（Kane-Mele）的相似之处，我们称这种不变的凯恩·梅勒（Kane-Mele）不变，因此与凯恩 - 梅勒（Kane-Mele）的相似之处是与时间反转对称性的系统。每当所有Chern数量消失时，我们都证明了这种不变的等同于Chern-Simons轴耦合，并且在存在反转对称性的情况下，我们显示了如何从触发空间中的固定点上的反转操作员的特征值获得这种不变性。对于非平凡的Chern号码的一般情况，Chern-Simons Axion耦合项包含了K理论Kane-Mele不变的信息以及有关具有非读数Chern号码的频段的信息。为Chern-Simons轴耦合项提出了一个明确的公式，与K理论的Khey-Mele不变性相关联，并获得了与Kheory Kheory的关系，并获得了反转操作员特征值的公式。使用有效的汉密尔顿模型和第一原理计算，我们还表明，可以在Pnictides家族的轴突绝缘子中观察到散装波段反演和非平凡的K理论凯恩 - 梅尔不变指数的发生。特别是，我们证明，由于发现其他拓扑指标，例如量子旋转霍尔效应，间隙表面状态，表面量化了异常霍尔效应和手性铰链模式，因此可以将NPBI归类为轴突绝缘子。
Axion insulators are generally understood as magnetic topological insulators whose Chern-Simons axion coupling term is quantized and equal to $π$. Inversion and time reversal, or the composition of either one with a rotation or a translation, are symmetries which protect this invariant. In this work, we focus our attention on the composition of a 2-fold rotation with time reversal, and we show that insulators with this symmetry possess a Z2 invariant arising from Atiyah's real K-theory. We call this invariant the K-theory Kane-Mele invariant due to the similarities it has with the Kane-Mele invariant for systems with time-reversal symmetry. Whenever all Chern numbers vanish, we demonstrate that this invariant is equivalent to the Chern-Simons axion coupling, and in the presence of the inversion symmetry, we show how this invariant could be obtained from the eigenvalues of the inversion operator on its fixed points in momentum space. For the general case of non-trivial Chern numbers, the Chern-Simons axion coupling term incorporates information of the K-theory Kane-Mele invariant as well as information regarding bands with non-trival Chern numbers. An explicit formula in terms of K-theory generators is presented for the Chern-Simons axion coupling term, the relation with the K-theory Kane-Mele invariant is explained, and a formula in terms of eigenvalues of the inversion operator is obtained. Using an effective Hamiltonian model and first-principles calculations, we also show that the occurrence of bulk-band inversion and nontrivial K-theory Kane-Mele invariant index can be observed in axion insulators of the pnictides family. In particular, we demonstrate that NpBi can be classified as an axion insulator due to the detection of additional topological indicators such as the quantum spin Hall effect, gapped surface states, surface quantized anomalous Hall effect, and chiral hinge modes
