论文标题
超出对称指标的脆弱拓扑的几何方法
Geometric approach to fragile topology beyond symmetry indicators
论文作者
论文摘要
当考虑到更细的频段分区时，我们提出了一个系统地解决拓扑阶段的框架，而不仅仅是考虑由价和传导带跨越的两个子空间。专注于$ C_2 \ Mathcal {T} $ - 对称系统，这些系统引起了最近关注的对称系统，例如，在分层的Van-Waals石墨烯异质结构的背景下，我们将这些见解与Grassmannians和Flag品种的同型群体相关联，而这些见解又与同源性类别相对应的群体和Wilson-flow Chackes。我们还利用几何结构，即所谓的plücker嵌入，以诱导带状结构中的绕组，以促进非平凡的拓扑结构。具体而言，这直接与格拉斯曼尼亚人的参数化有关，该参数描述了任意带结构的分区，并嵌入了更好可管理的外部产品空间中。从物理的角度来看，我们的构造封装并阐明了超出对称指标的脆弱拓扑阶段的概念，以及当考虑到多个差距时会产生的频段节点的非亚伯式互惠编织。所采用的几何观点最重要的是直接且易于实现的方法，以构建模型的汉密尔顿人研究此类阶段，构成多功能理论工具。
We present a framework to systematically address topological phases when finer partitionings of bands are taken into account, rather than only considering the two subspaces spanned by valence and conduction bands. Focusing on $C_2\mathcal{T}$-symmetric systems that have gained recent attention, for example in the context of layered van-der-Waals graphene heterostructures, we relate these insights to homotopy groups of Grassmannians and flag varieties, which in turn correspond to cohomology classes and Wilson-flow approaches. We furthermore make use of a geometric construction, the so-called Plücker embedding, to induce windings in the band structure necessary to facilitate non-trivial topology. Specifically, this directly relates to the parametrization of the Grassmannian, which describes partitioning of an arbitrary band structure and is embedded in a better manageable exterior product space. From a physical perspective, our construction encapsulates and elucidates the concepts of fragile topological phases beyond symmetry indicators as well as non-Abelian reciprocal braiding of band nodes that arises when the multiple gaps are taken into account. The adopted geometric viewpoint most importantly culminates in a direct and easily implementable method to construct model Hamiltonians to study such phases, constituting a versatile theoretical tool.
