Observing the Quantum Hall Effect in 'Real' Space

“The real space observation of rather complex phenomena due to quantum mechanics is the key access to a descriptive understanding” of the world that governs quantum physics, Hashimoto continues. Hashimoto currently belongs to Tohoku University and to JST-ERATO in Sendai, Japan, but while he was at Hamburg University in Germany, he started experiments with Markus Morgenstern in a group led by Roland Wiesendanger. Getting support from theoretical groups at Universities of Warwick and Ryukyu, he and his collaborators finally succeeded in showing quantum Hall transition in “real” space. The results of the experiments are reported in Physical Review Letters: “Quantum Hall Transition in Real Space: From Localized to Extended States.”

The Hall effect results when an electric current flows in the presence magnetic field with a potential difference across an electrical conductor. As one might expect, the quantum Hall effect is a quantum-mechanical rendering - one that is observed in two-dimensional electron systems and at low temperatures. Hashimoto points out, “The quantum Hall effect as a paradigmatic and nicely tunable example of quantum phase transitions provides a very adaptable access to simple results of complex descriptions.”

According to Hashimoto, the experiments done in Hamburg represent “the first real space observation of a quantum Hall transition by performing scanning tunneling spectroscopy on ‘surface’ two-dimensional electron system.” He describes the system as operating at a temperature of 0.3 K and in a high magnetic field of up to 12 T.

As a result of these experiments, Hashimoto says that spatial resolution has been increased over other scanning probes by more than a full order of magnitude: “The resolution is now below relevant length scales to probe electronic wave function in quantum Hall regime and, consequently, we could observe for the first time the quantum phase transition from localized to extended states directly.”

While the measurements show the quantum Hall transition of how single particles behave in probing states well away from the Fermi level, they do not include many body electron-electron effects. These effects are also important when wants to create a picture of how the quantum world functions. However, Hashimoto points out that what the group found could possibly be extended to a many body system. He says, “In principle, our experiment can extend to two-dimensional electron system at Fermi level where electron-electron interaction can be strong, using p-type semiconductor sample. …We could reveal a wealth of further quantum phase transitions.”

With a p-type sample, Hashimoto continues, it would be possible to see greater energy resolution. He believes that if the findings could be expanded and applied in further experiments, it would be possible to truly address universal critical behavior at the quantum level, bringing us a better understanding of the fundamentals of quantum physics. And, Hashimoto points out, the experiments using a p-type sample are starting in a group led by Markus Morgenstern at Aachen University.

More Information: Katsushi Hashimoto, et. al. Quantum Hall Transition in Real Space: From Localized to Extended States. Physical Review Letters (2008). http://link.aps.or … t.101.256802

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