Liu Shuo, Gao Wenlong, Zhang Qian, Ma Shaojie, Zhang Lei, Liu Changxu, Xiang Yuan Jiang, Cui Tie Jun, Zhang Shuang
School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, UK.
Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province, College of Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China.
Research (Wash D C). 2019 Feb 5;2019:8609875. doi: 10.34133/2019/8609875. eCollection 2019.
Topological circuits, an exciting field just emerged over the last two years, have become a very accessible platform for realizing and exploring topological physics, with many of their physical phenomena and potential applications as yet to be discovered. In this work, we design and experimentally demonstrate a topologically nontrivial band structure and the associated topologically protected edge states in an RF circuit, which is composed of a collection of grounded capacitors connected by alternating inductors in the x and y directions, in analogy to the Su-Schrieffer-Heeger model. We take full control of the topological invariant (i.e., Zak phase) as well as the gap width of the band structure by simply tuning the circuit parameters. Excellent agreement is found between the experimental and simulation results, both showing obvious nontrivial edge state that is tightly bound to the circuit boundaries with extreme robustness against various types of defects. The demonstration of topological properties in circuits provides a convenient and flexible platform for studying topological materials and the possibility for developing flexible circuits with highly robust circuit performance.
拓扑电路是在过去两年中刚刚兴起的一个令人兴奋的领域，已成为实现和探索拓扑物理的一个非常容易理解的平台，其许多物理现象和潜在应用尚未被发现。在这项工作中，我们设计并通过实验证明了射频电路中的拓扑非平凡能带结构以及相关的拓扑保护边缘态，该电路由在x和y方向上通过交替电感连接的接地电容器集合组成，类似于Su-Schrieffer-Heeger模型。我们通过简单地调整电路参数，完全控制了拓扑不变量（即Zak相位）以及能带结构的带隙宽度。实验结果与模拟结果高度吻合，两者均显示出明显的非平凡边缘态，该边缘态紧密束缚于电路边界，对各种类型的缺陷具有极强的鲁棒性。电路中拓扑特性的证明为研究拓扑材料提供了一个方便且灵活的平台，并为开发具有高度鲁棒电路性能的柔性电路提供了可能性。
