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arXiv · 2107.06612

Predicting topological materials: symmetry-based indicator theories and beyond

Tiantian Zhang·Shuichi Murakami
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Abstract

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.

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Tiantian Zhang, Shuichi Murakami. 2021-07-14. Predicting topological materials: symmetry-based indicator theories and beyond. https://doi.org/10.1088/1361-6463%2Fac13f4

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