Noble Prize in Physics

•  The 2016 Nobel prize in physics has gone to David Thouless, Duncan Haldane and Michael Kosterlitz for their work on exotic states of matter.
• Their work explains the behavior of superconductors and superfluids by connecting these systems to topology.

About their work:

• Two-dimensional systems such as thin fluid films or single-layer materials can exhibit surprising effects, such as frictionless liquid flows or unconventional electrical behavior, and one-dimensional systems can be equally strange. To explain these phenomena, researchers have turned to vortices, curved surfaces, and other “topological” objects whose properties are stable and independent of the specific material involved.
• The topological framework is now used widely in predicting and characterizing new forms of matter, some of which offer stable states that could store information for a quantum computer.
• The role of topology in condensed matter physics was established in the early 1970s, when theorists were debating phase transitions in two-dimensional (2D) systems. Early work showed that conventional transitions (like those between water and ice) couldn't happen in two dimensions, but it was clear that some sort of abrupt change was occurring in, for example, liquid films that exhibited superfluidity below a critical temperature.
• To settle the debate, Kosterlitz and Thouless imagined a new form of phase transition based on vortices and other so-called topological defects. A vortex is a point in a magnetic film, for example, around which the magnetic spins of the atoms orient in a clockwise direction (orientation in the counterclockwise direction is called an antivortex).
• At high temperature, vortices and antivortices are plentiful, and the spins are disordered. However, Kosterlitz and Thouless showed that at low temperatures, vortices pair up with antivortices, partly canceling out their effect. As a result, the spins throughout the two-dimensional material are able to align with each other to a certain degree.
• This alignment is a form of “topological order” that also applies more generally to 2D systems of atoms (or electrons) that align an aspect of their quantum states—their quantum mechanical phases. As such, the Kosterlitz-Thouless (KT) transition explains the emergence of both superfluidity and superconductivity in two dimensions.
• A decade later, Thouless and colleagues again turned to topological arguments in explaining the quantum Hall effect (QHE). Discovered in 1980, the QHE is, like the classical Hall effect, an induced voltage in a current-carrying conductor exposed to a magnetic field. In the quantum case, however, the conductor is confined to two dimensions.
• When current flows longitudinally (north-south, say) through the conductor, a transverse (east-west) voltage is measured. Surprisingly, as the magnetic field increases gradually, the ratio of current to voltage (called the Hall conductance) increases by discrete jumps; the values are integer multiples of a fundamental conductance unit. This quantization does not depend on the type of material, or whether it contains any defects or impurities.
• The idea that topology could be used to characterize the phase of matter was also used by Haldane in his work on spin chains—one-dimensional systems of coupled atoms found in magnetic materials.
• These works started a trend that is completely dominant now, in which you can classify matter with a topological invariant and not care about the fine details. The most prominent example of this trend is the field of topological insulators—materials that only conduct electricity on their surfaces.
• Topology has grown into a robust sub-discipline in physics, where scientists use these concepts to develop new types of materials for computing, electrical transmission, and battery storage. Someday, materials based on these winners’ theoretical work might power Siri’s quantum-brained sass
• This theory has been a useful tool in many areas of physics, such as atomic physics and statistical mechanics. The decades of research mean that it is now possible for scientists to look at new phases of matter.
• Over the last ten years research in topology is revealing more and more secrets about how different matter behaves, and it could aid research in the areas of material science, electronics, and quantum computing

By: Vishal