论文标题
二维正方形晶格的两波段模型的结理论，具有高拓扑数
Knot theory for two-band model of two-dimensional square lattice with high topological numbers
论文作者
论文摘要
提出了针对二维方晶格的结理论，该理论阐明了具有高拓扑数的新二维材料的设计。我们考虑了一个两波段模型，重点是霍尔电导σxy= e^2/hbar*p，其中p是拓扑数，即所谓的pontrjagin索引。通过将周期动量组件KX和KY重新解释为两个纠缠结的字符串参数，我们发现P变成了结之间的高斯链接数。这导致了文献中典型的p-评估的成功重新启动：p = 0; {\ pm} 1。此外，借助此明确的结理论图片，我们修改了两波段模型以获得更高的拓扑数，p = 0; {\ pm} 1; {\ pm} 2。
A knot theory for two-dimensional square lattice is proposed, which sheds light on design of new two-dimensional material with high topological numbers. We consider a two-band model, focusing on the Hall conductance σxy = e^2/hbar*P, where P is a topological number, the so-called Pontrjagin index. By re-interpreting the periodic momentum components kx and ky as the string parameters of two entangled knots, we discover that P becomes the Gauss linking number between the knots. This leads to a successful re-derivation of the typical P-evaluations in literature: P = 0;{\pm}1. Furthermore, with the aid of this explicit knot theoretical picture we modify the two-band model to achieve higher topological numbers, P = 0;{\pm}1;{\pm}2.
