该研究团队发现四维（4D）中的拓扑电荷矢量，它们支配着二维（2D）准晶体的实空间拓扑结构，并揭示了其内在的守恒定律。研究人员通过相位解析和时域近场显微镜技术，对五边形等离子准晶格中的拓扑结构进行了操纵，并展示了其时间演化如何连续地调节其独特四维拓扑结构的二维投影。这项研究工作为实验探究四维及以上准晶体的热力学性质以及拓扑物理提供了一条途径。
据悉，根据诺特定理，物理系统中的对称性与守恒量相互交织。这些对称性往往决定着系统的拓扑结构，而系统的维度增加则会使拓扑结构变得更为复杂。准晶体既不具有平移对称性，也不具有全局旋转对称性，但它们本质上存在于一个更高维度的空间中，在这个空间里对称性得以重新显现。
附：英文原文
Title: Four-dimensional conserved topological charge vectors in plasmonic quasicrystals
Author: Shai Tsesses, Pascal Dreher, David Janoschka, Alexander Neuhaus, Kobi Cohen, Tim C. Meiler, Tomer Bucher, Shay Sapir, Bettina Frank, Timothy J. Davis, Frank Meyer zu Heringdorf, Harald Giessen, Guy Bartal
Issue&Volume: 2025-02-07
Abstract: 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.
Source: https://www.science.org/doi/10.1126/science.adt2495