论文标题
两个独立的Su-Schrieffer链的产物产生了二维Chern绝缘子
The product of two independent Su-Schrieffer-Heeger chains yields a two-dimensional Chern insulator
论文作者
论文摘要
在复杂的自由费米子的复杂拓扑阶段的背景下，我们提供了广泛的观察。在此过程中，我们评论了由矢量束的外部张量产物引起的不相等阶段中的产物结构的存在 - 矢量束的外部张量产物 - 这种结构尚未在凝结的文献中探讨。 BOTTECICTICITICITICITICITICITICITICITICTICTICTICTICE的形式是由给定相构建的广义Dirac Monopole的形式，相当于具有相同阶段的Dirac Monopole相的乘积。复杂的K理论共同学环是存储这些阶段信息的一种自然方式，其评分对应于Clifford Symmetries Modulo $ 2 $的数量。 Künneth公式使我们能够得出这样的结果，即对于带绝缘子，su-schrieffer-heeger（ssh）链中的一个维度允许一个维度，使人们可以生成$ d $ d $维的brillouin区域的K-cohomology。特别是，我们发现在独立动量方向上两个SSH链的乘积产生了二维Chern绝缘子。获得的结果以统一的方式在所有空间维度上都将电荷持续带绝缘子及其拓扑不变性的相关拓扑阶段联系起来。
We provide an extensive look at Bott periodicity in the context of complex gapped topological phases of free fermions. In doing so, we remark on the existence of a product structure in the set of inequivalent phases induced by the external tensor product of vector bundles -- a structure which has not yet been explored in condensed-matter literature. Bott periodicity appears in the form of a generalized Dirac monopole built out of a given phase, which is equivalent to the product of a Dirac monopole phase with that same given phase. The complex K-theory cohomology ring is presented as a natural way to store the information of these phases, with a grading corresponding to the number of Clifford symmetries modulo $2$. The Künneth formula allows us to derive the result that, for band insulators, the Su-Schrieffer-Heeger (SSH) chain in one dimension allows one to generate the K-cohomology of the $d$-dimensional Brillouin zone. In particular, we find that the product of two SSH chains in independent momentum directions yields a two-dimensional Chern insulator. The results obtained relate the associated topological phases of charge-conserving band insulators and their topological invariants in all spatial dimensions in a unified way.
