Four-dimensional conserved topological charge vectors in plasmonic quasicrystals

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.