The discovery of quadrupole topology opens a new horizon in the study of topological phenomena. However, the existing experimental realizations of quadrupole topological insulators in symmorphic lattices with $\pi$ fluxes often break the protective mirror symmetry. Here, we present a theory for anomalous quadrupole topological insulators in nonsymmorphic crystals without flux using two-dimensional sonic crystals with $p4gm$ and $p2gg$ symmetry groups as concrete examples. We reveal that the anomalous quadrupole topology is protected by two orthogonal glide symmetries in square or rectangular lattices. The distinctive features of the anomalous quadrupole topological insulators include: (i) minimal four bands below the topological band gap, (ii) nondegenerate gapped Wannier bands and special Wannier sectors with gapped composite Wannier bands, and (iii) quantized Wannier band polarizations in these Wannier sectors. With no need for flux insertion, the protective glide symmetries are well preserved in the sonic-crystal realizations where higher-order topological transitions can be triggered by symmetry or geometry engineering.

中文翻译：

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二维非同形声晶体中的异常四极拓扑绝缘子

四极拓扑的发现为拓扑现象的研究开辟了新的视野。然而，在同构晶格中四极拓扑绝缘子的现有实验实现具有$\pi$通量经常破坏保护镜的对称性。在这里，我们提出了一种非二维晶体的无通量的异常四极拓扑绝缘子的理论。$p4G米$ 和 $p2GG$对称组作为具体示例。我们揭示了异常的四极拓扑受到正方形或矩形格子中两个正交滑移对称性的保护。异常四极拓扑绝缘子的显着特征包括：（i）拓扑带隙以下的最小四个带；（ii）非退化带隙的Wannier带和特殊的带复合Wannier带的Wannier扇区，以及（iii）这些中的量化Wannier带极化万尼尔部门。无需插入助焊剂，在声波晶体实现中可以很好地保留保护性滑行对称性，在这些实现中，对称性或几何工程可以触发更高阶的拓扑转换。