Abstract

According to the mathematical classification of topological band structures, there exist a number of fascinating topological states in dimensions larger than three with exotic boundary phenomena and interesting topological responses. While these topological states are not accessible in condensed matter systems, recent works have shown that synthetic systems, such as photonic crystals or electric circuits, can realize higher-dimensional band structures. Here, we argue that, because of its symmetry properties, the 4D spinless topological insulator is particularly well suited for implementation in these synthetic systems. We explicitly construct a 2D electric circuit lattice, whose resonance frequency spectrum simulates the 4D spinless topological insulator. We perform detailed numerical calculations of the circuit lattice and show that the resonance frequency spectrum exhibits pairs of 3D Weyl boundary states, a hallmark of the nontrivial topology. These pairs of 3D Weyl states with the same chirality are protected by classical time-reversal symmetry that squares to +1, which is inherent in the proposed circuit lattice. We also discuss how the simulated 4D topological band structure can be observed in experiments.

Highlights

  • With the great success of topological band theory in condensed matter physics [1,2,3,4,5,6], recent research has branched out to the study of topological bands in synthetic lattices, such as, photonic crystals [7,8,9,10], ultracold atomic gases [11,12,13,14,15,16], and electric circuit networks [17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34]

  • These 4D topological states exhibit many interesting phenomena, e.g., quantized nonlinear responses [40,41,42,43,44,45], topological charge pumping, and in-gap boundary modes with protected level crossings [46]. These 4D states cannot be realized in condensed matter systems, which are limited to three spatial dimensions

  • We propose in this paper an experimental realization of the 4D spinless topological insulator in a periodic electric circuit composed of inductors (L), capacitors (C), and operational amplifiers

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Summary

Introduction

With the great success of topological band theory in condensed matter physics [1,2,3,4,5,6], recent research has branched out to the study of topological bands in synthetic lattices, such as, photonic crystals [7,8,9,10], ultracold atomic gases [11,12,13,14,15,16], and electric circuit networks [17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34]. An experimental realization of the 4D spinless topological insulator could allow to simulate chiral lattice gauge theory of high-energy physics [51,52,53].

Results
Conclusion

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