Predicting topological materials: symmetry-based indicator theories and beyond
Predicting topological materials: symmetry-based indicator theories and beyond
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DOI：
10.1088/1361-6463/ac13f4
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发表时间：
2021-07
期刊：
影响因子：
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通讯作者：
Tiantian Zhang;S. Murakami
中科院分区：
文献类型：
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作者：
Tiantian Zhang;S. Murakami
尽管基于对称性的指标公式在诊断高对称性点间存在带隙结构的拓扑状态方面具有较强的能力，但当相容性条件被违反时，该指标公式在诊断拓扑简并性方面存在缺陷。在这种情况下，我们只能通过配伍条件获得在某些高对称点或沿某些高对称线是否存在能带简并的信息。在对称性指标理论的框架下，提出了一种利用相容性违例系统的子群的对称性指标公式诊断拓扑带交叉以获得整体拓扑信息的算法。本文通过两个具有时间反转对称性的无自旋系统中保留不同拓扑状态的实例，对该算法进行了更简单的解释，讨论了基于对称的指标理论的局限性，并进一步讨论了该算法在具有时间反转对称性的有自旋系统中的应用。
Though symmetry-based indicators formulae are powerful in diagnosing topological states with a gapped band structure at/between any high-symmetry points, it fails in diagnosing topological degeneracies when the compatibility condition is violated. In such cases, we can only obtain information of whether there is a band degeneracy at some high-symmetry points or along some high-symmetry lines by the compatibility condition. Under the framework of symmetry-based indicator theories, we proposed an algorithm to diagnose the topological band crossings in the compatibility condition-violating systems to obtain the whole topological information, by using the symmetry-based indicator formulae of their subgroups. In this paper, we reinterpret the algorithm in a simpler way with two material examples preserving different topological states in spinless systems with time-reversal symmetry, discuss the limitation of the symmetry-based indicator theories, and make further discussions on the algorithm applying in spinful systems with time-reversal symmetry.