Topology, a branch of mathematics, has become a cornerstone of modern physics, thanks to the extraordinary - and most importantly - reliable - properties it can impart to a material or system. Unfortunately, identifying topological systems, or even designing new topological systems, is often a tedious process that requires precise matching of physical systems to mathematical models.
Researchers at the University of Amsterdam and the École Normale Supérieure of Lyon have demonstrated a model-free method for identifying topological structures, enabling the discovery of new topological materials using purely experimental methods.
Topology consists of the properties of a system that are not changed by any "smooth deformation". As you can probably tell from this rather formal and abstract description, topology began as a branch of mathematics. Over the past few decades, however, physicists have shown that the mathematical basis of topology can have very real consequences. Topological effects can be found in a variety of physical systems, from individual electrons to large-scale ocean currents.
To give a concrete example: In the field of quantum matter, topology has made a name for itself with so-called topological insulators. These materials do not conduct electricity through their bodies, but electrons move freely along their surfaces or edges. This surface conduction will persist, unhindered by defects in the material, as long as you don't do something drastic, like change the entire atomic structure of the material. In addition, the current on the surface or edge of a topological insulator has a fixed direction (depending on the electron spin), which is also determined by the topological properties of the electronic structure.
These topological features can have very useful applications, and topology has become one of the frontier fields of materials science. In addition to identifying topological materials in nature, parallel research efforts are focused on designing synthetic topological materials from the bottom up. The topological edge states of mechanical structures known as "metamaterials" offer unparalleled opportunities to achieve reliable responses in wave guidance, sensing, computing and filtering.
Research in this area has been slow due to the lack of experimental methods to study the topological properties of systems. The necessity to match mathematical models to physical systems limits our research into materials that already have theoretical descriptions and creates a bottleneck in identifying and designing topological materials. To solve this problem, Xiaofei Guo and Corentin Cules of the Laboratory of Machine Materials at the University of Amsterdam teamed up with Marcelo Guzman, David Carpentier and Denis Bartolo of the Ecole Normale Supérieure in Lyon.
Xiaofei Guo said: "So far, most experiments have been done to prove theories or demonstrate theoretical predictions in journals. We found a way to measure topologically protected soft or brittle spots in unknown mechanical metamaterials without the need for modeling. Our method allows for practical exploration and characterization of material properties without delving into complex theoretical frameworks."
The researchers demonstrated their approach using a mechanical metamaterial made from a network of rotors (rotatable rigid rods) connected by elastic springs. The topology in these systems can make certain areas of the metamaterial particularly squishy or stiff.
Bartolo explains: "We realized that locally selective probing of materials can provide us with all the necessary information to reveal soft or brittle spots in the structure, even in regions far away from our probing. Using this, we developed highly practical protocols that apply to a wide range of materials and metamaterials."
By probing individual rotors in the metamaterial and tracking the resulting displacement and elongation in the system, the researchers identified different "mechanical molecules": sets of rotors and springs that move as a unit. Similar to electrostatic systems, they then calculated each molecule's effective "polarization" based on its motion. In the presence of topological features, this polarization suddenly changes direction, making the inherent topology easily identifiable.
The researchers applied their method to a variety of mechanical metamaterials, some of which were topologies known from previous studies, while others were new structures for which there was no associated mathematical model. The results show that experimentally determined polarizations are very effective in pointing out topological features.
This model-free approach is not limited to mechanical systems, the same approach can also be applied to photonic or acoustic structures. It will make topology more accessible to a wider range of physicists and engineers and make it easier to build functional materials beyond laboratory demonstrations.
Compiled source: ScitechDaily