Once thought impossible, quasicrystals reveal 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. His findings puzzled the scientific community initially, as the material appeared disorganized on a small scale but displayed a distinct, symmetrical pattern at larger scales.
At the time, this structure was deemed impossible, and Shechtman faced skepticism. However, theoretical explanations emerged from Prof. Dov Levine and his advisor Prof. Paul Steinhardt, then at the University of Pennsylvania. They proposed that quasicrystals follow a periodic structure, but in a higher-dimensional space beyond our familiar three dimensions.
Higher-Dimensional Insights into Quasicrystals
The concept of higher spatial dimensions extends our three-dimensional space by adding directions perpendicular to length, width, and height. While difficult to visualize, these extra dimensions can be studied through projections or shadows, similar to observing a cube’s shadow on a two-dimensional surface.
An example of a four-dimensional object is the tesseract, often called a hypercube. Just as a cube comprises six square facets, a tesseract comprises eight cubic cells. This object, while invisible to us, can be understood through its lower-dimensional projections.
New Research Sheds Light on Hidden Structures
Recent research, published in Science, sheds new light on quasicrystals by investigating their topological properties. The study, led by Prof. Guy Bartal and Dr. Shai Tsesses from the Technion, along with colleagues from the University of Stuttgart and University of Duisburg-Essen, demonstrated that higher-dimensional crystals determine not only the mechanical properties of quasicrystals but also their topological characteristics.
The Role of Topology in Understanding Quasicrystals
Topology is a branch of mathematics that studies properties unchanged by continuous deformations. In higher-dimensional spaces, this branch examines objects’ properties beyond three dimensions. It plays a crucial role in fields like understanding the universe’s structure and developing quantum computing algorithms.
The researchers used quasiperiodic interference patterns of electromagnetic surface waves to study topological properties.他们 found that despite appearing different, these patterns shared identical topological properties in two dimensions. The only way to distinguish between them was by referring to their original higher-dimensional crystals.
Time and the Unexpected Behavior of Surface Waves
The study also uncovered an intriguing phenomenon: two distinct topological patterns of surface waves appeared identical when measured after a specific time interval. This interval was short, measured in attoseconds—a billionth of a billionth of a second. The original theory by Levine and Steinhardt explains this phenomenon as a competition between topological and thermodynamic properties of the crystals.
Advanced Techniques Unlock New Possibilities
The findings were achieved using two methods: near-field scanning optical microscopy performed by Dr. Kobi Cohen in Prof. Guy Bartal’s lab, and two-photon photoemission electron microscopy conducted in collaboration with the University of Stuttgart and University of Duisburg-Essen.
The discoveries reported in this manuscript pave the way for new methods to measure the thermodynamic properties of quasicrystals. Future research aims to expand these findings to other physical systems and explore the interplay between thermodynamic and topological properties further.
This research has implications for using quasicrystals to represent, encode, and transfer information due to their unique higher-dimensional topological properties.
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.
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).
As we continue to explore the mysteries of quasicrystals, these findings not only deepen our understanding of materials but also open new avenues for technological advancement. If this research piques your interest, consider subscribing to Archynetys for more updates on cutting-edge science and technology.
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