Zhang Weixuan, Cao Wenhui, Qian Long, Yuan Hao, Zhang Xiangdong
Key Laboratory of advanced optoelectronic quantum architecture and measurements of Ministry of Education, Beijing Institute of Technology, Beijing, China.
Beijing Key Laboratory of Nanophotonics & Ultrafine Optoelectronic Systems, School of Physics, Beijing Institute of Technology, Beijing, China.
Nat Commun. 2025 Jan 2;16(1):198. doi: 10.1038/s41467-024-55425-1.
Topolectrical circuits have emerged as a pivotal platform for realizing static topological states that are challenging to construct in other systems, facilitating the design of robust circuit devices. In addition to spatial dimensionality, synergistic engineering of both temporal and spatial degrees in circuit networks holds tremendous potential across diverse technologies, such as wireless communications, non-reciprocal electronics and dynamic signal controls with exotic space-time topology. However, the realization of space-time modulated circuit networks is still lacking due to the necessity for flexible modulation of node connections in both spatial and temporal domains. Here, we propose a class of topolectrical circuits, referred to as topolectrical space-time circuits, to bridge this gap. By designing and applying a time-varying circuit element controlled by external voltages, we can construct circuit networks exhibiting discrete space-time translational symmetries in any dimensionality, where the circuit dynamical equation is in the same form with time-dependent Schrödinger equation. Through the implementation of topolectrical space-time circuits, three distinct types of topological space-time crystals are experimentally demonstrated, including the (1 + 1)-dimensional topological space-time crystal with midgap edge modes, (2 + 1)-dimensional topological space-time crystal with chiral edge states, and (3 + 1)-dimensional Weyl space-time semimetals. Our work establishes a solid foundation for the exploration of intricate space-time topological phenomena and holds potential applications in the field of dynamically manipulating electronic signals with unique space-time topology.
拓扑电路已成为实现静态拓扑状态的关键平台，这些状态在其他系统中难以构建，有助于设计稳健的电路器件。除了空间维度外，电路网络中时间和空间维度的协同工程在多种技术中具有巨大潜力，如无线通信、非互易电子学以及具有奇异时空拓扑的动态信号控制。然而，由于需要在空间和时间域中灵活调制节点连接，时空调制电路网络的实现仍然缺乏。在此，我们提出一类拓扑电路，称为拓扑时空电路，以弥合这一差距。通过设计和应用由外部电压控制的时变电路元件，我们可以构建在任何维度上都表现出离散时空平移对称性的电路网络，其中电路动力学方程与含时薛定谔方程具有相同形式。通过实现拓扑时空电路，实验展示了三种不同类型的拓扑时空晶体，包括具有带隙边缘模式的(1 + 1)维拓扑时空晶体、具有手性边缘态的(2 + 1)维拓扑时空晶体以及(3 + 1)维外尔时空半金属。我们的工作为探索复杂的时空拓扑现象奠定了坚实基础，并在利用独特时空拓扑动态操纵电子信号领域具有潜在应用。
