A quantized microwave quadrupole insulator with topologically protected corner states
A quantized microwave quadrupole insulator with topologically protected corner states
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DOI：
10.1038/nature25777
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发表时间：
2018-03-15
期刊：
影响因子：
64.8
通讯作者：
Bahl, Gaurav
中科院分区：
文献类型：
--
作者：
Peterson, Christopher W.;Benalcazar, Wladimir A.;Bahl, Gaurav
晶体中的电极化理论将绝缘体的偶极矩定义为与其电子基态(1，2)相关的Berry相(几何相)。这个概念不仅解决了如何计算晶体中偶极矩的长期难题，而且解释了绝缘体和超导体中的拓扑能带结构，包括量子反常霍尔绝缘体(3，4)和量子自旋霍尔绝缘体(5-7)，以及量子化绝热泵浦过程(8-10)。最近的一项理论研究扩展了Berry相框架，也解释了更高的电子多极矩(11)，揭示了以前没有观察到的更高阶拓扑相的存在。在这里，我们通过实验演示了这类预测材料中的一员--一种量子化的四极拓扑绝缘体--使用千兆赫兹频率可重新配置的微波电路生产的。我们使用光谱测量和识别由体拓扑产生的角态来确认非平凡的拓扑相。此外，我们通过将晶格的边缘从拓扑区形变到平凡区来检验临界预测，即这些角态受到体拓扑结构的保护，而不是由于表面伪影。我们的结果提供了确凿的证据，证明了高阶拓扑绝缘子具有抗无序和变形的独特形式的稳健性。
The theory of electric polarization in crystals defines the dipole moment of an insulator in terms of a Berry phase (geometric phase) associated with its electronic ground state(1,2). This concept not only solves the long-standing puzzle of how to calculate dipole moments in crystals, but also explains topological band structures in insulators and superconductors, including the quantum anomalous Hall insulator(3,4) and the quantum spin Hall insulator(5-7), as well as quantized adiabatic pumping processes(8-10). A recent theoretical study has extended the Berry phase framework to also account for higher electric multipole moments(11), revealing the existence of higher-order topological phases that have not previously been observed. Here we demonstrate experimentally a member of this predicted class of materials-a quantized quadrupole topological insulator-produced using a gigahertz-frequency reconfigurable microwave circuit. We confirm the non-trivial topological phase using spectroscopic measurements and by identifying corner states that result from the bulk topology. In addition, we test the critical prediction that these corner states are protected by the topology of the bulk, and are not due to surface artefacts, by deforming the edges of the crystal lattice from the topological to the trivial regime. Our results provide conclusive evidence of a unique form of robustness against disorder and deformation, which is characteristic of higher-order topological insulators.