Shao L B, Liu Q, Xiao R, Yang Shengyuan A, Zhao Y X
National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China.
Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China.
Phys Rev Lett. 2021 Aug 13;127(7):076401. doi: 10.1103/PhysRevLett.127.076401.
Although topological artificial systems, like acoustic and photonic crystals and cold atoms in optical lattices were initially motivated by simulating topological phases of electronic systems, they have their own unique features such as the spinless time-reversal symmetry and tunable Z_{2} gauge fields. Hence, it is fundamentally important to explore new topological phases based on these features. Here, we point out that the Z_{2} gauge field leads to two fundamental modifications of the conventional k·p method: (i) The little co-group must include the translations with nontrivial algebraic relations. (ii) The algebraic relations of the little co-group are projectively represented. These give rise to higher-dimensional irreducible representations and therefore highly degenerate Fermi points. Breaking the primitive translations can transform the Fermi points to interesting topological phases. We demonstrate our theory by two models: a rectangular π-flux model exhibiting graphenelike semimetal phases, and a graphite model with interlayer π flux that realizes the real second-order nodal-line semimetal phase with hinge helical modes. Their physical realizations with a general bright-dark mechanism are discussed. Our finding opens a new direction to explore novel topological phases unique to crystalline systems with gauge fields and establishes the approach to analyze these phases.
尽管拓扑人工系统，如声学和光子晶体以及光学晶格中的冷原子，最初是受电子系统拓扑相模拟的启发，但它们具有自身独特的特性，如无自旋时间反演对称性和可调谐的Z₂规范场。因此，基于这些特性探索新的拓扑相具有根本重要性。在这里，我们指出Z₂规范场导致了对传统k·p方法的两个基本修改：（i）小余群必须包括具有非平凡代数关系的平移。（ii）小余群的代数关系是射影表示的。这些产生了高维不可约表示，从而导致高度简并的费米点。打破原初平移可以将费米点转变为有趣的拓扑相。我们通过两个模型来展示我们的理论：一个呈现类石墨烯半金属相的矩形π通量模型，以及一个具有层间π通量的石墨模型，该模型实现了具有铰链螺旋模式的实二阶节线半金属相。讨论了它们用一般亮暗机制的物理实现。我们的发现为探索具有规范场的晶体系统特有的新型拓扑相开辟了一个新方向，并建立了分析这些相的方法。
