Fourth-Order Topological Insulator via Dimensional Reduction

TL;DR

This paper demonstrates how a 4D higher-order topological insulator can be mapped onto a 1D aperiodic array, revealing corner states and topological properties inherited from higher dimensions, thus enabling exploration of multi-dimensional topological physics in lower-dimensional systems.

Contribution

The authors introduce a dimensional reduction method to emulate 4D topological insulators in 1D systems, revealing corner states and topological features in a new lower-dimensional context.

Findings

Observation of zero-energy corner states in the 1D array

Mapping of 4D topological properties onto a 1D aperiodic system

Identification of topologically protected resonances

Abstract

The properties of topological systems are inherently tied to their dimensionality. Higher-dimensional physical systems exhibit topological properties not shared by their lower dimensional counterparts and, in general, offer richer physics. One example is a d-dimensional quantized multipole topological insulator, which supports multipoles of order up to 2^d and a hierarchy of gapped boundary modes with topological 0-D corner modes at the top. While multipole topological insulators have been successfully realized in electromagnetic and mechanical 2D systems with quadrupole polarization, and a 3D octupole topological insulator was recently demonstrated in acoustics, going beyond the three physical dimensions of space is an intriguing and challenging task. In this work, we apply dimensional reduction to map a 4D higher-order topological insulator (HOTI) onto an equivalent aperiodic 1D array sharing the same spectrum, and emulate in this system the properties of a hexadecapole topological insulator. We observe the 1D counterpart of zero-energy states localized at 4D HOTI corners - the hallmark of multipole topological phase. Interestingly, the dimensional reduction guarantees that one of the 4D corner states remains localized to the edge of the 1D array, while all other localize in the bulk and retain their zero-energy eigenvalues. This discovery opens new directions in multi-dimensional topological physics arising in lower-dimensional aperiodic systems, and it unveils highly unusual resonances protected by topological properties inherited from higher dimensions.