Intriguing physical properties of materials stem from their chemical constituents, whereas the connection between them is often not clear. Here, we uncover a general chemical classification for the two quantum phases in the honeycomb ABX structure-topological insulator (TI) and topological Dirac semimetal (TDSM). First, we find among the 816 (existing as well as hypothetical) calculated compounds, 160 TIs (none were noted before), 96 TDSMs, 282 normal insulators (NIs), and 278 metals. Second, based on this classification, we have distilled a simple chemical regularity based on compound formulas for the selectivity between TI and TDSM: the ABX compounds that are TDSM have B atoms (part of the BX honeycomb layers) that come from the periodic table columns XI (Cu, Ag, Au) or XII (Zn, Cd, Hg), or Mg (group II), whereas the ABX compounds whose B atoms come from columns I (Li, Na, K, Rb, Cs) or II (Ca, Sr, Ba) are TIs. Third, focusing on the ABX bismide compounds that are thermodynamically stable, we find a structural motif that delivers topological insulation and stability at the same time. This study opens the way to simultaneously design new topological materials based on the compositional rules indicated here.

中文翻译：

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蜂窝状化合物中的拓扑绝缘体与拓扑狄拉克半金属

材料有趣的物理特性源于它们的化学成分，而它们之间的联系通常并不明确。在这里，我们揭示了蜂窝状 ABX 结构拓扑绝缘体 (TI) 和拓扑狄拉克半金属 (TDSM) 中两个量子相的一般化学分类。首先，我们在 816 种（现有的和假设的）计算化合物中发现了 160 种 TI（以前没有注意到）、96 种 TDSM、282 种正常绝缘体 (NI) 和 278 种金属。其次，基于这种分类，我们基于 TI 和 TDSM 之间选择性的化合物公式提炼出一个简单的化学规律：TDSM 的 ABX 化合物具有来自元素周期表列的 B 原子（BX 蜂窝层的一部分） XI（Cu、Ag、Au）或 XII（Zn、Cd、Hg）或 Mg（II 组），而 B 原子来自列 I（Li、Na、K、Rb、Cs）或 II（Ca、Sr、Ba）的 ABX 化合物是 TI。第三，关注热力学稳定的 ABX 双胺化合物，我们发现了一个结构基序，可以同时提供拓扑绝缘和稳定性。这项研究为基于此处指出的组成规则同时设计新的拓扑材料开辟了道路。