拓扑电氮化物磷灰石中的高阶拓扑晶体绝缘相和量子化铰链电荷
Higher-Order Topological Crystalline Insulating Phase and Quantized Hinge Charge in Topological Electride Apatite
摘要：
在高阶拓扑绝缘体中，体电子态和表面电子态是带隙的，同时出现受空间对称性保护的无带隙铰链态。在这里，我们表明，通过从头计算的La磷灰石晶体是一个高阶拓扑晶体绝缘体。它是一个一维的空穴结构，其中沿$c$轴的一维间隙空穴支撑着阴离子电子，这些一维通道中的电子态可以用一维的Su-Schrieffer-Heeger模型很好地近似.当晶体被切割成六棱柱时，120个$^\circ$铰链支持无间隙铰链状态，其填充被量化为2/3。这种填充的量化来自拓扑学的起源。我们发现，填充的量化值取决于构成晶体的基本块。磷灰石由三角形块体组成，这对于在铰链处产生非平凡分数电荷至关重要。
英文摘要：
In higher-order topological insulators, bulk and surface electronic states are gapped, while there appear gapless hinge states protected by spatial symmetry. Here we show by ab initio calculations that the La apatite electride is a higher-order topological crystalline insulator. It is a one-dimensional electride, in which the one-dimensional interstitial hollows along the $c$ axis support anionic electrons, and the electronic states in these one-dimensional channels are well approximated by the one-dimensional Su-Schrieffer-Heeger model. When the crystal is cleaved into a hexagonal prism, the 120$^\circ$ hinges support gapless hinge states, with their filling quantized to be 2/3. This quantization of the filling comes from a topological origin. We find that the quantized value of the filling depends on the fundamental blocks that constitute the crystal. The apatite consists of the triangular blocks, which is crucial for giving nontrivial fractional charge at the hinge.
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