论文标题
双曲线拓扑结束器
Hyperbolic Topological Band Insulators
论文作者
论文摘要
最近，瓷砖呈负弯曲双曲机平面的双曲线晶格作为合成物质的新范式出现，其能级的特征是在四（或更高）维度动量空间中的带结构。为了探索双曲线理论中产生的未知拓扑方面，我们在这里介绍了双曲线拓扑带绝缘子的基本模型：双曲线haldane模型和双曲线Kane-Mele模型；两者都通过用八块代替其欧几里得对应物的六边形细胞获得。通过在位置和动量空间中计算拓扑不变性，它们的非平凡拓扑结构可以揭示出来。通过比较状态的散装和边界密度，通过对边缘激发的传播进行建模以及它们对无序的稳健性，可以证明宽大的对应关系。
Recently, hyperbolic lattices that tile the negatively curved hyperbolic plane emerged as a new paradigm of synthetic matter, and their energy levels were characterized by a band structure in a four- (or higher-)dimensional momentum space. To explore the uncharted topological aspects arising in hyperbolic band theory, we here introduce elementary models of hyperbolic topological band insulators: the hyperbolic Haldane model and the hyperbolic Kane-Mele model; both obtained by replacing the hexagonal cells of their Euclidean counterparts by octagons. Their non-trivial topology is revealed by computing topological invariants in both position and momentum space. The bulk-boundary correspondence is evidenced by comparing bulk and boundary density of states, by modelling propagation of edge excitations, and by their robustness against disorder.
