At the time, the existence of such a material was considered impossible, requiring years of effort to convince the scientific community of its validity. The first physicists to provide a theoretical framework for the discovery were Professor Dov Levine, then a doctoral student at the University of Pennsylvania and now a faculty member in the Technion Physics Department, and his advisor, Professor Paul Steinhardt. Their key insight was that quasicrystals were, in fact, periodic-but in a spatial dimension higher than their physical existence. This concept enabled the prediction of their mechanical and thermodynamic properties.
The idea of higher spatial dimensions extends beyond the familiar three-length, width, and height-by incorporating additional directions perpendicular to all three. While visualizing such dimensions is challenging, their mathematical representation is well established. A well-known example of a four-dimensional geometric object is the tesseract or hypercube. Just as a cube consists of six square facets, a tesseract is composed of eight cubic cells. Though it cannot be directly visualized, its projection can be represented much like the shadow of a three-dimensional cube on a two-dimensional surface.
A recent study published in Science by researchers from the Technion, the University of Stuttgart, and the University of Duisburg-Essen in Germany further explores this concept. Led by Professor Guy Bartal and Dr. Shai Tsesses from the Andrew and Erna Viterbi Faculty of Electrical and Computer Engineering, along with Professor Harald Giessen from the University of Stuttgart and Professor Frank Meyer zu Heringdorf from the University of Duisburg-Essen, the research team demonstrated that the properties of quasiperiodic crystals extend beyond mechanics to include topology.
Topology, a branch of mathematics concerned with properties that remain invariant under continuous deformations, plays a key role in understanding higher-dimensional spaces. These principles aid in studying complex structures, from the organization of the universe to the design of quantum computing algorithms. By analyzing quasiperiodic interference patterns of electromagnetic surface waves, the researchers found that despite variations in appearance, the patterns could not be distinguished solely based on their two-dimensional topological properties. Instead, the differences could only be understood by referring to a higher-dimensional crystalline structure.
This finding aligns with the explanation originally proposed by Levine and Steinhardt, which built upon earlier work by British mathematician Sir Roger Penrose, a 2020 Nobel Prize laureate in Physics, and later formalized by Nicolaas de Bruijn.
An additional discovery revealed another intriguing phenomenon: two distinct topological surface wave patterns appeared identical when observed after a specific time interval. This interval was measured in attoseconds-a billionth of a billionth of a second. Once again, the theory of Levine and Steinhardt provided a framework for understanding this effect as a result of competition between topological and thermodynamic properties within the crystal.
These findings were obtained through two advanced experimental techniques: near-field scanning optical microscopy performed in Professor Bartal's lab by Dr. Kobi Cohen, and two-photon photoemission electron microscopy, a collaborative effort between the University of Stuttgart and the University of Duisburg-Essen. The results open new pathways for investigating the thermodynamic characteristics of quasiperiodic crystals. The researchers plan to extend their work to other physical systems and further examine the interplay between thermodynamic and topological properties. The potential applications of quasicrystals' unique topological properties could lead to new methods for encoding, representing, and transmitting information.
The research was supported by the European Research Council (ERC), the German Research Foundation (DFG), Germany's Federal Ministry of Education and Research (BMBF), BW Stiftung, Carl-Zeiss Stiftung, the Russell Berrie Nanotechnology Institute at the Technion (RBNI), the Helen Diller Quantum Center at the Technion (HDQC), and the Sarah and Moshe Zisapel Nanoelectronics Center at the Technion (MNFU).
Research Report:Four-dimensional conserved topological charge vectors in plasmonic quasicrystals
Related Links
Technion-Israel Institute of Technology
Understanding Time and Space
| Subscribe Free To Our Daily Newsletters |
| Subscribe Free To Our Daily Newsletters |
