Crucially, the existence of these protected edge modes can be traced to the physics of the bulk material. One can summarize the mathematical description of wave propagation inside a topological insulator as an intricate knot and that outside it as a simple loop. The knot must be cut at the edges to match the ‘untwisted’ wave propagation outside. Cutting the knot allows modes that have otherwise forbidden frequencies to be present.

中文翻译：

---

波浪转角。

至关重要的是，这些受保护边缘模式的存在可以追溯到大块材料的物理特性。人们可以将拓扑绝缘体内部波传播的数学描述概括为一个复杂的结，而在其外部作为一个简单的环。结必须在边缘切割以匹配外部“未扭曲”的波传播。解开结可以让原本禁止频率的模式出现。