Greetings from the fourth dimension: Scientists get a glimpse into 4D crystal structures using surface wave patterns

In April 1982, Professor Dan Shechtman of the Technion -Israel Institute of Technology made the discovery that he later won the 2011 Nobel Prize in Chemistry: Quasi-periodic Crystal. Diffraction measurements made with electron microscopy revealed that the new material appeared to be “confusing” on a smaller scale, but apparent ordering and symmetry on a larger scale.

This form of material was deemed impossible and it took years to convince the scientific community of the validity of the discovery. The first physicist to explain this finding in theory was Professor Dov Levine, a doctoral student at the University of Pennsylvania, currently a faculty member of the Technion School of Physics and his advisor, Professor Paul Stanhalt. did.

The key insight that enabled their explanation was that in practice the quasi-crystals were periodic, but they were on a higher dimension than what they physically existed. Using this realization, physicists were able to explain and predict the mechanical and thermodynamic properties of quasi-signals.

The concept of higher spatial dimensions expands the familiar three-dimensional space (length, width, height) by introducing additional orientations perpendicular to all three. This is difficult to visualize because we only perceive the world around us as three-dimensional space, which makes it even more difficult to measure. An example of a 4D object is Tesseract, also known as Hypercube.

Tesseract consists of eight cubic cells, just as the cubes are made up of six square facets. Tesseract cannot be fully visualized, but you can express it through its projection, just like seeing the shadows of a 3D cube on two-dimensional paper.

A new study published in Science, together with researchers from The Technion, along with the University of Stuttgart and Duisburg-Essen in Germany, shed new light on the phenomenon. Their research is led by Professors Guy Bartal and Andrew Elna Viterbi of Electrical and Computer Engineering, Harald Gisen at the University of Stuttgart, and Professor Frank Meier Zu Herringdorf at the University of Dewisburg – Essen, Research The group demonstrated that high-dimensional crystals not only determine the mechanical properties of quasi-periodic crystals, but also the topological properties.

Topology is a field of mathematics that investigates geometric properties that do not change under continuous deformation. The topology of high-dimensional space focuses on the properties of objects in three or more dimensions, allowing for example to study the structure of the universe and help develop quantum computing algorithms.

Researchers examined the quasi-peripheral interference patterns of electromagnetic surface waves and, to their surprise, discovered that although the patterns appear different, they cannot be distinguished using two-dimensional topological properties. did. They found that the only way to distinguish patterns is to refer to the “original” high-dimensional crystals.

This understanding is based on previous findings by British mathematician Ir Roger Penrose (Physics of the 2020 Nobel Prize winner), and explained by Levine and Steinhardt, later conveyed by Nicolaa de Bruin. matches.

Researchers also discovered another interesting phenomenon. Two different topological patterns of surface waves appeared identical when measured after a specific time interval. This interval was very short, measured in attoseconds. This is one billionth of a second. The original theory by Levine and Steinhardt again describes this phenomenon as a “competition” between the topology and thermodynamic (energy) properties of a crystal.

Findings were achieved using two methods. It was performed using optical optical microscopy performed by Dr. KobiCohen in the Guy Bartal laboratory and two-photon photoemission electron microscopy measured in a collaboration between Stuttgart and Duisburg-Essen University. Germany. The findings reported in the manuscript pave the way for new methods for measuring the thermodynamic properties of quasi-periodic crystals.

In the near future, researchers plan to expand their findings to other physical systems and explore more in-depth the interactions between thermodynamics and topological properties. Potentially, the unique, high-dimensional topological properties of quasicrystals can be used in the future to represent, encode, and transfer information.