Circuit implementation of a four-dimensional topological insulator

You Wang,Baile Zhang,Hannah M Price,Y D Chong,Y D Chong

doi:10.1038/s41467-020-15940-3

You Wang, Baile Zhang + Show 3 more

Open Access

https://doi.org/10.1038/s41467-020-15940-3

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Abstract

The classification of topological insulators predicts the existence of high-dimensional topological phases that cannot occur in real materials, as these are limited to three or fewer spatial dimensions. We use electric circuits to experimentally implement a four-dimensional (4D) topological lattice. The lattice dimensionality is established by circuit connections, and not by mapping to a lower-dimensional system. On the lattice’s three-dimensional surface, we observe topological surface states that are associated with a nonzero second Chern number but vanishing first Chern numbers. The 4D lattice belongs to symmetry class AI, which refers to time-reversal-invariant and spinless systems with no special spatial symmetry. Class AI is topologically trivial in one to three spatial dimensions, so 4D is the lowest possible dimension for achieving a topological insulator in this class. This work paves the way to the use of electric circuits for exploring high-dimensional topological models.

Highlights

The classification of topological insulators predicts the existence of high-dimensional topological phases that cannot occur in real materials, as these are limited to three or fewer spatial dimensions
In the symmetry-based classification of topological phases[3,4,5,6,7], Class AI includes time-reversal (T) symmetric, spinless systems that are not protected by any special spatial symmetries
Using impedance measurements that are equivalent to finding the local density of states (LDOS), we show that the 4DQH phase hosts surface states on the 3D surface, while the conventional insulator phase has only bulk states

Summary

Introduction

The classification of topological insulators predicts the existence of high-dimensional topological phases that cannot occur in real materials, as these are limited to three or fewer spatial dimensions. Topological phases have been implemented in a range of engineered systems including cold atom lattices[13], photonic structures[14], acoustic and mechanical resonators[15,16], and electric circuits[17,18,19,20,21,22,23,24,25,26,27,28] Some of these platforms can realise lattices that are hard to achieve in real materials, raising the intriguing prospect of using them to create high-dimensional topological insulators. Since electric circuits are defined in terms of lumped (discrete) elements and their interconnections, lattices with genuine high-dimensional structure can be explicitly constructed by applying the appropriate connections[33,34,35] In this way, we experimentally implement a 4D lattice hosting the first realisation of a Class AI topological insulator[5,6], which has no counterpart in three or fewer spatial dimensions. In those experiments the second Chern number in 4D is not truly independent of the first Chern numbers in 2D, which are nonzero

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