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Emergence and full 3D-imaging of nodal boundary Seifert surfaces in 4D topological matter
Communications Physics ( IF 5.4 ) Pub Date : 2019-10-29 , DOI: 10.1038/s42005-019-0235-4
Linhu Li , Ching Hua Lee , Jiangbin Gong

The topological classification of nodal links and knot has enamored physicists and mathematicians alike, both for its mathematical elegance and implications on optical and transport phenomena. Central to this pursuit is the Seifert surface bounding the link/knot, which has for long remained a mathematical abstraction. Here we propose an experimentally realistic setup where Seifert surfaces emerge as boundary states of 4D topological systems constructed by stacking 3D nodal line systems along a 4th quasimomentum. We provide an explicit realization with 4D circuit lattices, which are freed from symmetry constraints and are readily tunable due to the dimension and distance agnostic nature of circuit connections. Importantly, their Seifert surfaces can be imaged in 3D via their pronounced impedance peaks, and are directly related to knot invariants like the Alexander polynomial and knot Signature. This work thus unleashes the great potential of Seifert surfaces as sophisticated yet accessible tools in exotic bandstructure studies.



中文翻译:

节点边界Seifert表面在4D拓扑物质中的出现和全3D成像

节点链接和结的拓扑分类吸引了物理学家和数学家,无论是数学上的优雅还是对光学和传输现象的影响。追求链接的核心是塞弗(Seifert)表面,它长期以来一直是数学上的抽象。在这里,我们提出了一种实验上现实的设置,其中,塞弗特表面作为4D拓扑系统的边界状态而出现,该边界系统是通过沿4阶叠加3D节点线系统而构建的。我们提供了4D电路格的显式实现,该网格不受对称约束的限制,并且由于电路连接的尺寸和距离不可知的性质而易于调整。重要的是,它们的Seifert表面可以通过其明显的阻抗峰值以3D形式成像,并与结不变式(如亚历山大多项式和结签名)直接相关。因此,这项工作释放了Seifert表面的巨大潜力,成为异国情调的带状结构研究中复杂而易用的工具。

更新日期:2019-10-29
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