Wow: Nobel Prize instead of gravitational waves was given for topology

“Topology is fate,” he said, and pulled his trousers. First on one leg, then on the other.
- Neil Stephenson

In early October, the Nobel laureates in physics were announced in Stogkolm, Sweden. Three British scientists received the prize for their contribution to the development of this science: David Thouless, Duncan Haldane and Michael Kosterlitz for the “theoretical discoveries of topological phase transitions and topological phases of matter”. Physicists were upset because everyone believed that the prize would go to various members of the LIGO collaboration who announced this year the first discovered gravitational waves, the source of which was the confluence of black holes. This year, the Nobel Committee took the practical side, and awarded scientists who developed a method to create controlled “holes” or defects in quantum mechanical states of matter, known as condensates.

Their research has led to a breakthrough in materials science and condensed matter physics, and promises a revolution in electronics. For the 24th consecutive year, a reward has been awarded to a group of people, and for the 53rd consecutive year, only men receive an award.



The universe can be studied from two sides: there is Einstein's General Theory of Relativity, which controls gravity and space-time evolution, and there is quantum mechanics, which controls three other fundamental forces and all interactions, phases and properties of matter. The physical community happily discussed the first detection of gravitational waves, predicted long ago by Einstein's theory, and found this year - and at this time other amazing discoveries, breakthroughs and practical work in the field of creating new states of matter were made. Most people are familiar with the three states of matter - solid, liquid and gaseous, but there is also a fourth one that appears when a gas is very hot: plasma. Conversely, in nature, in some types of substance, there is another state that occurs during strong cooling: condensate. Unlike other states, condensates exhibit unique properties that are not found anywhere else in nature.
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Quantum physics revolutionized our world view and taught us the following:
• Nature is discrete, not continuous, and consists of separate fundamental particles, quanta.
• Quanta have inherent properties that cannot be changed: spin, electric charge, color charge, aroma, etc.
• When creating composite systems, new properties appear - for example, the orbital angular momentum, isospin and non-zero physical dimensions.

But one of the interesting points is the fact that these properties of particles and their interaction can manifest themselves completely differently, if we limit them to two dimensions - a flat surface - instead of three.



For a long time, it was believed that superconductivity and superfluidity, the two properties of certain substances, which manifest themselves at low temperatures and are expressed in zero resistance and zero viscosity, respectively, work only in three-dimensional materials. But in the 1970s, Michael Kosterlitz and David Towless found not only that these properties can appear in two-dimensional layers, but also a phase transition mechanism, due to which superconductivity disappears at sufficiently high temperatures. With a decrease in the number of degrees of freedom and dimensions, forces and interactions, quantum mechanical systems become easier to study. Equations that are complex for three dimensions are simplified for two. The equations, whose solution for three dimensions was not found, have a solution for two.



Many particles, quasiparticles, and particle systems behave like “topological defects”, similar to either “holes” (for a 0-dimensional defect) or “strings” (for a 1-dimensional defect), passing through two-dimensional or three-dimensional space . Applying topology to these low-temperature systems, one can predict new topological states of matter.


At ultralow temperatures, topological defects in two-dimensional condensed systems often pair together, which is not observed at high temperatures.

The nature of the transition from low-temperature states (where pairs of vortices form) to high-temperature states (where pairs become independent) obey the rules of the Kosterlitz-Tauless transition. The combination of quantum physics with topology leads to the fact that a lot of interesting physical processes occur discretely, in steps. The conductivity of the thin material occurs in steps. Chains of small magnets behave topologically. The phase transition rules apply equally to all materials in two dimensions. In the 1980s, Kosterlitz discovered bonds in conductivity, and Duncan Haldane found topological properties of chains of small magnets. And although the application of these properties extends to other areas of physics - statistical mechanics, atomic physics, and, we hope, will soon spread to electronics and quantum computers - physics, explaining the discrete behavior of matter in smaller dimensions, works according to the same topological rules as any mathematical system.


The topology studies the properties varying in steps, like the number of holes in these objects.

These new properties can manifest themselves only at low temperatures or in very strong magnetic fields, but this does not make them less fundamental than commonly observed properties. The quantum Hall effect, the fact that the "whole" quantum magnets are topological, and the "half-goals" is not, and that you can determine the properties of a quantum magnet by studying its faces, and caused the prize to be won by our trinity. Based on their research, new, unexpected types of matter were discovered, including topological properties, which also manifest themselves in three-dimensional materials. Topological dielectrics, topological superconductors and topological metals are being actively studied today, and have the potential to revolutionize electronics and computing as soon as they can be controlled.



Alfred Nobel during the creation of the Nobel Prize decided that it should be given for discoveries responsible for "the greatest benefits to humanity." And this science is not only proven, but is already completely on the path of changing our lives. And although there are a large number of worthy teams, people and discoveries, this year's Nobel Prize reminds us of two main reasons why we develop basic science: knowledge and social benefits for humanity. This year, a glimpse into the past of what amazing things about matter in extreme conditions were discovered, shows how far our knowledge has progressed. A look into the future for the application of these discoveries inspires us to search for new generations of quantum technologies. Uncertain future depends on us.