Second Chern crystals in four-dimensional synthetic translation space with inherently nontrivial topology

TL;DR

This paper introduces and demonstrates a four-dimensional topological crystal in synthetic translation space, inherently nontrivial due to its topology, with observable boundary and dislocation modes, advancing topological wave physics.

Contribution

It presents the first experimental realization of a second Chern crystal in four-dimensional synthetic space with guaranteed nontrivial topology.

Findings

Observation of one-dimensional gapless dislocation modes

Robustness of boundary modes confirmed experimentally

Inherent nontrivial topology regardless of configuration

Abstract

Topological states, first known as quantum Hall effect or Chern insulating crystal, have been generalized to many classical wave systems where potential applications such as robust waveguiding, quantum computing and high-performance lasers are expected. However, a crystal can be either topologically trivial or nontrivial, depending on its detailed configuration, and one needs to carefully design the structure and calculate its topological invariant before the actual applications. Here, we theoretically study and experimentally demonstrate the second Chern crystal in a four-dimensional space by introducing two extra synthetic translation dimensions. Due to the inherently nontrivial topology of the synthetic translation space, this abstract four-dimensional crystal is guaranteed to be topologically nontrivial regardless of the detailed configuration. The dimensional hierarchy of gapless boundary modes can be deduced by dimension reduction. Remarkably, one-dimensional gapless dislocation modes are observed and their robustness is confirmed in our experiments. This ubiquitous phenomenon in synthetic translation space provides perspectives on the findings of topologically nontrivial crystals and inspires the designs of classical wave devices.