Four-dimensional conserved topological charge vectors in plasmonic quasicrystals

The symmetry and topology of physical systems are closely related to the symmetries governing the topological properties. Quasicrystals are ordered systems but have no translation or rotational symmetries. Theoretical work has shown that quasicrystals can be understood as the projection of a higher-dimensional crystal onto a lower-dimensional space. Tsesses et al. developed a plasmonic-based system in which to study the implications of that projection for topological invariants. When going into four-dimensional space and projecting it down into two dimensions, the complex dynamics of light waves on the plasmonic quasicrystal exhibited motions of four-dimensional topological charge vectors and associated topological charge conservation laws. This approach allows the study of topological systems in higher dimensions. — Ian S. Osborne

According to Noether’s theorem, symmetries in a physical system are intertwined with conserved quantities. These symmetries often determine the system topology, which is made ever more complex with increased dimensionality. Quasicrystals have neither translational nor global rotational symmetry, yet they intrinsically inhabit a higher-dimensional space in which symmetry resurfaces. Here, we discovered topological charge vectors in four dimensions (4D) that govern the real-space topology of 2D quasicrystals and reveal their inherent conservation laws. We demonstrate control over the topology in pentagonal plasmonic quasilattices, mapped by both phase-resolved and time-domain near-field microscopy, showing that their temporal evolution continuously tunes the 2D projections of their distinct 4D topologies. Our work provides a route to experimentally probe the thermodynamic properties of quasicrystals and topological physics in 4D and above.