Topology in higher dimensions
In condensed-matter systems, the band structure of a material has often been equated with functionality. However, consideration of the topology of the band structure now provides a route to developing a functionality that goes far beyond the expected properties of the materials. Using electromagnetic metamaterials as building blocks, Ma et al. realized a five-dimensional generalization of a topological Weyl semimetal. Along with the three real momentum dimensions, these included two bi-anisotropy material parameters as synthetic dimensions to demonstrate both linked Weyl surfaces and Yang monopoles. The metamaterial platform provides a powerful route to explore the exotic physics associated with higher-order topological phenomena.
Science, abi7803, this issue p. 572
Abstract
Generalization of the concept of band topology from lower-dimensional to higher-dimensional (n > 3) physical systems is expected to introduce new bulk and boundary topological effects. However, theoretically predicted topological singularities in five-dimensional systemsтАФWeyl surfaces and Yang monopolesтАФhave either not been demonstrated in realistic physical systems or are limited to purely synthetic dimensions. We constructed a system possessing Yang monopoles and Weyl surfaces based on metamaterials with engineered electromagnetic properties, leading to the observation of several intriguing bulk and surface phenomena, such as linking of Weyl surfaces and surface Weyl arcs, via selected three-dimensional subspaces. The demonstrated photonic Weyl surfaces and Weyl arcs leverage the concept of higher-dimension topology to control the propagation of electromagnetic waves in artificially engineered photonic media.
