This “Impossible” Crystal Is Changing What We Know About Reality
- Once thought impossible, quasicrystals revealed a hidden order that challenges our understanding of materials.
- Dan Shechtman of the Technion – Israel Institute of Technology made a groundbreaking discovery that would later earn him the 2011 Nobel Prize in Chemistry: the quasiperiodic crystal.
- At the time, this type of structure was thought to be impossible, and Shechtman faced years of skepticism before the scientific community accepted his findings.
Once thought impossible, quasicrystals revealed a hidden order that challenges our understanding of materials.
A Revolutionary Discovery in Crystallography
In April 1982, Prof. Dan Shechtman of the Technion – Israel Institute of Technology made a groundbreaking discovery that would later earn him the 2011 Nobel Prize in Chemistry: the quasiperiodic crystal. When he examined the material using electron diffraction, it appeared “disorganized” on a small scale, yet displayed a distinct, symmetrical pattern when viewed at a larger scale.
At the time, this type of structure was thought to be impossible, and Shechtman faced years of skepticism before the scientific community accepted his findings. The first physicists to provide a theoretical explanation were Prof. Dov Levine, then a doctoral student at the
Higher-Dimensional Insights into Quasicrystals
The concept of higher spatial dimension extends our familiar three-dimensional space – length, width, and height – by introducing additional directions that are perpendicular to all three. This is difficult to visualize, as we can only perceive the world around us as a three-dimensional space, and even more challenging to measure. An example of a four-dimensional object is the tesseract, also known as hypercube. Just as a cube consists of six square facets, a tesseract comprises eight cubic cells. Although we cannot fully visualize a tesseract, we can represent it through its projections, much like looking at the shadow of a three-dimensional cube on a two-dimensional piece of paper.
New Research Sheds Light on Hidden Structures
In a new manuscript published in Science, researchers from the Technion, together with the University of Stuttgart and University of Duisburg-Essen in Germany, shed new light on this phenomenon. In their study, led by Prof. Guy Bartal and Dr. Shai Tsesses from the Andrew and Erna Viterbi Faculty of Electrical and Computer Engineering, Prof. Harald Giessen from the University of Stuttgart, and Prof. Frank Meyer zu Heringdorf from the University of Duisburg-Essen, the research group demonstrated that not only do the higher dimensional crystals dictate the mechanical properties of quasiperiodic crystals – they also determine their topological properties.
The Role of Topology in Understanding Quasicrystals
Topology is a branch of mathematics that investigates the geometric properties that remain unchanged under continuous deformations. The topology of higher-dimensional spaces focuses on the properties of objects in more than three dimensions and can assist, for example, in studying the structure of the universe and developing quantum computing algorithms. The researchers examined quasiperiodic interference patterns of electromagnetic surface waves and discovered, to their surprise, that although the patterns appeared different, their topological properties in two dimensions could not be used to differentiate between them. They found the only way to distinguish between the patterns was by referring to an “original” higher-dimensional crystal.
This understanding agrees with the explanation given by Levine and Steinhardt, which was based on an earlier discovery by British mathematician, Sir Roger Penrose (2020 Nobel Prize laureate in Physics) and later conveyed by Nicolaas de Bruijn.
Time and the Unexpected Behavior of Surface Waves
The researchers also discovered another intriguing phenomenon: two different topological patterns of surface waves appeared identical when measured after a specific time interval. This interval was extremely short, measured in attoseconds – a billionth of a billionth of a second. The original theory by Levine and Steinhardt again explains this phenomenon as a “competition” between the topological and thermodynamic (energetic) properties of the crystals.
Advanced Techniques Unlock New Possibilities
The findings were achieved using two methods: near-field scanning optical microscopy conducted in Prof. Guy Bartal’s lab by Dr. Kobi Cohen and two-photon photoemission electron microscopy, measured in collaboration between the University of Stuttgart and the University of Duisburg-Essen in Germany. The discoveries reported in the manuscript pave the way for new methods to measure the thermodynamic properties of quasiperiodic crystals.
In the near future, the researchers plan to expand their findings to other physical systems and delve deeper into the interplay between thermodynamic and topological properties. Potentially, the unique higher-dimensional topological properties of quasicrystals could be used in the future to represent, encode, and transfer information.
Reference: “Four-dimensional conserved topological charge vectors in plasmonic quasicrystals” by 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 and Guy Bartal, 6 February 2025, Science.
DOI: 10.1126/science.adt2495
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).