论文标题
美元
$\mathbb{Z}_2$-projective translational symmetry protected topological phases
论文作者
论文摘要
对称是拓扑阶段的基础。在存在量规场的情况下，将预测代表空间对称性，这可能会改变其代数结构并产生新的拓扑阶段。我们表明，$ \ mathbb {z} _2 $ project代表翻译对称操作员采用独特的换向关系，并变得依赖于双重非词素对称性的动量。结合其他内部或外部对称性，它们产生了许多异国情调的拓扑结构，例如在布里鲁因区域的整个边界上的堕落性，固定在布里鲁因区角的单个四倍越野点以及在每个动量点上的kramers变性。有趣的是，可以通过打破一个原始翻译来提高狄拉克点的临界性，从而导致拓扑绝缘体相，其中边缘带具有möbius扭曲。我们的工作开辟了一个新的研究领域，用于探索受项目代表的太空组保护的拓扑阶段。
Symmetry is fundamental to topological phases. In the presence of a gauge field, spatial symmetries will be projectively represented, which may alter their algebraic structure and generate novel topological phases. We show that the $\mathbb{Z}_2$ projectively represented translational symmetry operators adopt a distinct commutation relation, and become momentum dependent analogous to twofold nonsymmorphic symmetries. Combined with other internal or external symmetries, they give rise to many exotic band topology, such as the degeneracy over the whole boundary of the Brillouin zone, the single fourfold Dirac point pinned at the Brillouin zone corner, and the Kramers degeneracy at every momentum point. Intriguingly, the Dirac point criticality can be lifted by breaking one primitive translation, resulting in a topological insulator phase, where the edge bands have a Möbius twist. Our work opens a new arena of research for exploring topological phases protected by projectively represented space groups.
