Crystalline Euler phases in topological condensed matter systems

近年来，人们发现了一类新的依赖于多能隙条件的拓扑材料。这些功能在倒易空间中的非阿贝尔编织属性，其中带节点被称为“欧拉类”的拓扑不变量的存在保护免受湮灭。该项目将涉及对无自旋和有自旋情况下所有可能的二维和三维晶体对称操作的系统研究，目的是绘制出所有可能的晶体欧拉相。

Recently, a new class of topological materials that depend on multi-gap conditions have been discovered. These feature non-Abelian braiding properties in reciprocal space, where band nodes are protected against annihilation by the existence of a topological invariant termed the 'Euler class'. The project will involve a systematic investigation of all possible two- and three-dimensional crystalline symmetry operations for both spinless and spinful cases, with the aim of mapping out all possible crystalline Euler phases.