Octupole corner state in a three-dimensional topological circuit

Shuo Liu,Wenlong Gao,Shuang Zhang,Cheng Yang,Qian Zhang,Shaojie Ma,Tie Jun Cui,Oubo You,Lei Zhang,Yuanjiang Xiang

doi:10.1038/s41377-020-00381-w

Abstract

Higher-order topological insulators (HOTIs) represent a new family of topological materials featuring quantized bulk polarizations and zero-dimensional corner states. In recent years, zero-dimensional corner states have been demonstrated in two-dimensional systems in the form of quadrupole modes or dipole modes. Due to the challenges in designing and constructing three-dimensional systems, octupole corner modes in 3D have not been observed. In this work, we experimentally investigate octupole topological phases in a three-dimensional electrical circuit, which can be viewed as a cubic lattice version of the Hofstadter model with a π-flux threading each plaquette. We experimentally observe in our higher-order topological circuit a 0D corner state manifested as a localized impedance peak. The observed corner state in the electrical circuit is induced by the octupole moment of the bulk circuit and is topologically protected by anticommuting spatial symmetries of the circuit lattice. Our work provides a platform for investigating higher-order topological effects in three-dimensional electrical circuits.

Highlights

Topological phases of matter possessing quantized invariants have attracted growing interest in the field of condensed matter physics and in classical systems, such as photonics and acoustics, and have shown great potential in lasing[1,2,3], quantum computing[4,5], and robust signal transmission in optical[6,7,8], acoustic[9,10], and mechanical[11,12] systems
Higher-order topological insulators (HOTIs) are mostly studied in 2D systems that host a quadrupole corner state, such as 2D microwave circuits[19], lowfrequency electrical circuits[20], photonic crystals[21,22,23,24,25], mechanical systems[26], and acoustic systems[27]
We experimentally observe the third-order topological corner state induced by the octupole moment in a

Summary

Introduction

Topological phases of matter possessing quantized invariants have attracted growing interest in the field of condensed matter physics and in classical systems, such as photonics and acoustics, and have shown great potential in lasing[1,2,3], quantum computing[4,5], and robust signal transmission in optical[6,7,8], acoustic[9,10], and mechanical[11,12] systems. While most of the research interests for topological insulators have focused on protected nontrivial localized modes one dimension lower than the bulk material, the recent emergence of higherorder topological insulators (HOTIs) shows the possibility of further dimensional reduction of the edge states[13,14,15,16,17,18]. These quantized higher-order multipole moments are localized at the intersection of the edges of a square The 3D topological corner mode has been demonstrated very recently[28,29,30,31]; some of these modes result from the nontrivial Zak phase of 3D bulk states[28], which is of a very different origin than octupole modes.

Methods

Results

Conclusion