Topolectrical space-time circuits

TL;DR

This paper introduces topolectrical space-time circuits that utilize time-varying elements to realize topological states with complex space-time symmetries, enabling experimental demonstration of various topological space-time crystals.

Contribution

It proposes a new class of circuits with controllable time-varying elements to create and study topological phenomena in space-time, bridging a gap in current circuit technology.

Findings

Demonstrated (1+1)D topological space-time crystal with edge modes

Realized (2+1)D topological space-time crystal with chiral edge states

Established (3+1)D Weyl space-time semimetals in circuits

Abstract

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 new class of topolectrical circuits, referred to as topolectrical space-time circuits, to bridge this gap. By designing and applying a novel 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 Schrodinger 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