On October 4, 2016 (September 4, 2016 lunar calendar), the "topology" that won the Nobel Prize in Physics: opening the door to the study of strange substances. On October 4, 2016 Beijing time, the 2016 Nobel Prize in Physics has just been announced! The winners are David Thouless, Duncan Haldane and Michael Kosterlitz. This year's Nobel Prize in Physics is awarded to David J. Thouless of the University of Washington in the United States, and the other half to F. Duncan M. Haldan of Princeton University and J. Michael Kosterlitz of Brown University. To reward them for "theoretical discoveries in topological phase transitions and topological materials". Strange phenomena in the two-dimensional world This year's Physics Prize winners have opened the door to the unknown world of the study of exotic states of matter, their work has led to breakthroughs in the theory of matter science and led to new horizons in the development of new materials. David Solis, Duncan Haldane and Mike Kosterlitz have used advanced mathematical methods to explain strange phenomena in unusual phases (or states) of matter, such as superconductors, superfluids or ultra-thin magnetic films. Kosterlitz and Solis have studied phenomena in the two-dimensional world, simply on a plane, or inside extremely thin layers. The real world, by contrast, is a three-dimensional world, with three dimensions: length, width and height. Haldane also studies extremely fine current materials, which can be thought of as one-dimensional. Physical phenomena that occur in the two-dimensional world are very different from those in the three-dimensional world we are familiar with. Even very thin matter contains millions of atoms, and even if the behavior of each atom can be explained by the principles of quantum mechanics, when large numbers of atoms are gathered together, they exhibit completely different strange properties. On the two-dimensional plane, the anomalous behavior of similar atoms after clustering has been continuously observed, and today, condensed matter physics, which specializes in studying such phenomena, has become an important field of physics. This year's three winners have made ground-breaking discoveries by applying mathematical concepts of topology, a mathematical concept that describes properties that vary in integers. Using this tool, this year's winners achieved unexpected results that opened new doors to research and led directly to the introduction of new and crucial concepts in multiple fields of physics. At low temperatures, you can "see" quantum mechanics. In essence, all matter is governed by quantum physics. Gases, liquids, and solids are all common phases of matter in which quantum effects are often overwhelmed by random atomic motions. But at extremely low temperatures (which is very close to absolute zero - 273 degrees Celsius), matter takes on a very bizarre phase and exhibits unusual behavior. Quantum mechanics, which normally works only on a microscopic scale, suddenly becomes "visible" at such low temperatures. When the temperature changes, common phases of matter also change with each other. For example, water ice is composed of a regular crystal structure. Once the temperature rises, it melts and completes the phase transition from solid to liquid. Compared to solid, the liquid phase is a more chaotic phase. And when we look at the two-dimensional world, we find a rather unfamiliar world. At low temperatures, some strange phenomena occur. For example, under such conditions, one of the fundamental properties of all material materials, electrical resistance, suddenly disappears. You observe this curious phenomenon: in superconductors, currents do not encounter electrical resistance, while in superfluids, a vortex never slows down, it spins forever. The first person to systematically study superfluids was the Russian scientist Pyotr Kapitsa in the 1930s. At that time, Kapitsa cooled helium-4 to minus 271 degrees Celsius and observed the phenomenon of the liquid flowing upward along the walls of the container. In other words, he observed the strange properties of superfluids after the viscosity has completely disappeared. For this achievement, Kapitsa was awarded the Nobel Prize in Physics in 1978. Since then, scientists have created several different types of superfluids in the lab. Superfluid liquid helium, superconducting films, magnetic thin layers, and conductive nanowires are just some of the new phases of matter that are currently being studied. The answer from the double vortex Researchers have long believed that thermodynamic disturbances destroy all order in matter in a two-dimensional plane, even at absolute zero. But in the early 1970s, David Solis and Mike Kosterlitz met in Birmingham, England, and decided to challenge this mainstream view together. They chose the two-dimensional in-plane phase transition as their research topic, according to the two men themselves, mainly out of curiosity, and Kosterlitz out of ignorance. Their collaboration led to a new understanding of the phase transition of matter and is considered one of the most important achievements in condensed matter physics in the 20th century. Their theory is now called the "KT phase transition" (Kosterlitz-Solis phase transition) or BKT phase transition, and the extra "B" here stands for Vadim Berezinskii, a late Russian physicist who proposed a similar theoretical idea. The topological phase transition is not a conventional phase transition, like that of water ice and liquid water. The factor that plays a key role in the topological phase transition is the tiny vortices in the planar material. At low temperatures they form tight "pairs". As the temperature rises, the phase transition occurs: these two small pairs of vortices suddenly move away from each other and move independently in the material. The beauty of this theory is that it can be applied to a variety of different materials in low dimensions, which means that the KT phase transition theory is universal. It has now become an important tool, not only for condensed matter, but also for other fields of physics, such as atomic physics and statistical mechanics. The theory behind the KT phase transition has also been developed by the original proponents and later generations and confirmed in experiments. Topology Answers Topology describes properties that remain unchanged when an object is stretched, twisted, or deformed, rather than torn apart. Topologically speaking, a ball and a bowl belong to the same category, because a spherical block of clay can be transformed into a bowl. However, a bagel with a hole in the middle and a coffee cup with a hole in the handle belong to another category. Of course, they can also be reshaped into each other's shapes. Therefore, a topological object can contain a hole, or two, or three, or four... but the number must be an integer. This goes a long way in describing the phenomenon of conductivity that exists in the quantum Hall effect, because the only change in each step of the quantum Hall effect is a multiple change of an integer. In the quantum Hall effect, electrons move relatively freely between semiconductor layers, forming a topological quantum fluid. As with the new properties that usually emerge when many particles come together, electrons in topological quantum fluids also show some surprising characteristics. Looking at only a small part of it, we can't be sure if a coffee cup has a hole. Similarly, observing only a part of it, we can't be sure if electrons have formed a topological quantum fluid. However, conductivity describes the collective motion of electrons, and because of the topology, each step change is different. Another feature of topological quantum fluids is that their boundaries have unusual properties. These have been predicted theoretically and have since been confirmed experimentally. Another milestone occurred in 1988, when Duncan Haldane discovered that topological quantum fluids could form in thin semiconductor layers, even in the absence of magnetic fields. Haldane said he never expected his theoretical model to be confirmed experimentally, but in 2014, his theoretical model was validated in an experiment in which atoms were cooled to almost zero degrees. New topological materials in development In earlier research, Duncan Haldane made a prediction that shocked experts in the field starting in 1982. In a theoretical study of magnetic chains of atoms that appear in some materials, Haldane found that the characteristics of atomic magnets determine the different properties of atomic chains. In quantum physics, there are two types of atomic magnets, odd and even. Haldane showed that even-numbered magnetic chains are topological, while even-numbered magnetic chains are not. As with topological quantum fluids, it is impossible to determine whether a chain of atoms belongs to a topology by simply examining a small part of it. And, as in the case of quantum fluids, topological properties reveal themselves at the edges. Here, that is, at the end of the atomic chain, because the quantum properties lie at the end of a topological chain. At first, no one believed Haldane's reasoning about atomic chains. Because the researchers believed that they had a complete understanding of atomic chains. But it turned out that Haldane had discovered the first instance of a new type of topological material. Today, this has become an active area of research in condensed matter physics. Quantum Hall liquids and magnetic atomic chains are both included in this new set of topological states. Later, researchers discovered several other unexpected topological states of matter, not confined to atomic chains, but in ordinary three-dimensional materials. Topological insulators, topological superconductors, and topological metals are now hot topics. For the past decade, these techniques have been at the forefront of condensed matter physics research, and it is hoped that topological materials can be applied to a new generation of electronic superconductors or future quantum computers. The current research is revealing the secrets of the substance discovered by this year's Nobel laureate.