Research conducted by the Quantum Dynamics Unit at Okinawa Institute of Science and Technology Graduate University (OIST) in Japan could represent an important step in understanding two-dimensional semiconductors. The unit’s latest paper, published in Physical Review Letters, describes anomalies in the behavior of electrons in an electrons-on-liquid helium two-dimensional system.

The OIST system is maintained at a temperature close to absolute zero (-272.75°C or 0.4K) to keep the helium liquefied. Extraneous electrons are bound to the helium surface because their presence causes slight changes in the orbits of helium electrons, inducing a subtle positive charge at the helium surface. At the same time, free electrons lack the energy required to penetrate the surface to enter the liquid. The resulting system is ideal for studying various electron properties, as it has virtually zero impurities, and thus avoids artifacts caused by defects of surface and structure, or due to the presence of other chemical elements. Prof. Denis Konstantinov, head of the Quantum Dynamics Unit, and his team studied conditions under which electrons can violate selection rules regulating transitions from one state to another.

In a macro-world, transitions from one state to another are perceived as happening gradually. For example, a person traveling from town A to town B can make an infinite number of stops. In micro-world that is not always the case. Properties, such as energy, position, speed and color, can be quantized; i.e. they can occur only in discrete quantities. In other words, the traveller can either be in town A or town B, but not somewhere in-between.

Since electron energy is quantized, electrons can occupy only specific energy levels. Quantum theory predicts that in a two-dimensional electron system where moving electrons are confined to one plane under a strong magnetic field, electrons also will be restricted to climbing only one step of the energy level ladder at a time. However, the experiments showed that electrons can jump to higher energy levels, skipping levels between. Konstantinov and his team are very excited about this discovery. “It is not everyday that we get a chance to observe the violation of quantum theory predictions,” he says.

The scientists applied a strong vertical magnetic field and then bombarded the system with microwave photons in order to study abnormalities in electron state changes. Under these conditions, selection rules seem to stop working. Konstantinov says his group had theorized that such a phenomenon is possible and now they have proven it.

Selection rules describe a theoretical, absolutely pure and homogenous system with no disorders. Real-life systems are more complex. In the case of electrons on helium, the system is pure and homogenous but the surface of liquid helium is nonetheless disturbed by capillary waves—ripples associated with the surface tension and similar to small, circular ripples in a pond when a pebble is tossed into the water. The height of these ripples is only the diameter of a hydrogen atom, but in combination with microwave radiation they create enough deviation from an ideal system for selection rules to change.

Conditions modeled in the Quantum Dynamics Unit’s experiment are similar to those that led to observations of zero resistance in semiconductors. However, the electrons on helium system is relatively simple and can be described mathematically with great precision. Studying this system will further the development of quantum physics and will contribute to our understanding of electrons and various electrical phenomena. Moreover, with some adjustments models, based on electrons on helium systems can be adapted to more complex systems, such as two-dimensional semiconductors.