A FLEET theoretical study this week found a "smoking gun" in the long search to find the topological magnetic monopole referred to as Berry curvature.This breakthrough is in the search for topological effect in non-equilibrium system.Dimi Culcer, UNSW's lead researcher, discovered an unusual Hall effect that is driven by an in-plane magnet field in semiconductor hole system. This phenomenon can only be traced back to the Berry curvature.(Inversely, both the anomalous Hall effect and the ordinary Hall effect require a magnetic field/magnetisation perpendicular the surface.The IEEE roadmap towards future electronics recently included enhanced topological effects that would make low-energy electronics suitable for large-scale operation at room temperature.ISOLATING REPONSE A BREAKTHROUGH MOMENT"Isolating topological reactions in'regular conductors" has been a difficult task for many years," A/Prof Dimi Crcer (UNSW) says. These topological responses are thought to be universal in solids.AdvertisementQuantized responses such as the quantum Hall or quantum spin-Hall effect provide a clear fingerprint on topology. However, these can only be observed in one-dimensional (1D), and are closely connected to the existence of edge state.There is a lot of literature that predicts topological contributions in'regular conductors', which are 2D and 3-dimensional systems. The anomalous Hall effect has never been clearly observed in transport measurements.This is due to two main reasons: (i) spin up and spin down electrons almost always make opposite contributions and they nearly cancel each other; and (ii) disorder overwhelms whatever is left.This long-standing problem is being addressed by the new FLEET paper. It identifies a two-dimensional system where the Berry curvature and only the Berry curve are responsible for the Hall sign linear in the applied in plane magnetic field.James Cullen, a UNSW PhD student, leads the research. "Remarkably all disorder contributions vanish. We aren't aware of any other multidimensional system in which such a thing is true." Its experimental measurement can be accessed by any laboratory with the latest technology worldwide. We expect high interest from experimentalists.BERRY CURVATURE, THE ANOMALOUS HALL EFFECT, AND TOPOLOGICAL MATERIALSAdvertisementThe researchers sought to find the mathematical clue called "Berry curvature", which is easily understood when we consider the notion of parallel transport, which appears regularly in geometry and general relativity.Dimi explains, "Think about a vector like an arrow we place somewhere on a solid object." Now we move the arrow about, making sure that it points at the same angle as the surface. This is akin to a person walking on the Earth's surface. After it has circled around, we eventually return the arrow to its starting point. We find that it points in a different direction, as it has magically rotated through an angle. This angle's size is determined by how the surface curves.Quantum mechanics uses wave functions instead of vectors. However, we can still describe dynamics using the same picture. The Berry curvature is also known as quantum mechanics.The famous Berry phase replaces the angle of rotation. It is named after Prof Sir Michael Berry who was a mathematical physicist who first formulated the problem in 1980s. Qian Niu, UT Austin, showed that the Berry curvature behaves in the same way as the coveted magnetic monopole, but in momentum space. This is the most common space condensed matter physicists think within.Because an electron's momentum changes when it is subject to an electric field, the Berry curvature causes topological effects in out of-equilibrium system. This causes the wave function to change slowly in the same manner that the 'arrow' rotates in parallel transport. A transverse (or Hall) current is then generated. According to the Onsager relations which are fundamental to nonequilibrium Physics, the Hall current doesn't dissipate any energy. Extreme cases include the quantum anomalous Hall phenomenon (QAHE), which is a quantum effect that affects the function of topological material. In this case, edge currents can flow with virtually zero electrical resistance.(Quantum) refers to a'step' transition within the transverse resistance (Hall), i.e. it changes in discrete steps instead of smoothly. While 'anomalous" refers to the phenomenon's absence from any applied magnetic field.Researchers are trying to improve QAHE to preserve topological behavior at higher temperatures. This would allow topological electronics to be suitable for operation at room temperature.Dimi states that "the significant reduction in electrical resistance allowed by room temperature QAHE would allow us significantly to reduce the power consumption of electronic devices."
