Landau Level Wave Functions Revealed
October 2, 2012

Researchers Reveal Internal Ring-like Structure Of Landau Levels

April Flowers for - Your Universe Online

For the first time since Nobel Prize winner Lev Landau conceived the theoretical existence of quantum levels that determine electron behavior in strong magnetic fields, scientists have directly imaged the phenomenon.

The research team, which included scientists from the University of Warwick and Tohoku University, used scanning tunneling spectroscopy — a spatially resolved probe that interacts directly with the electrons — to reveal the internal ring-like structure of the Landau levels at the surface of a semiconductor.

The largest challenge the team faced was to have sufficient spatial resolution in order to overcome the intrinsic disorder in the material. This disorder usually only allows the observation of smeared out "drift" states instead of a clear image of the Levels.

Landau originally predicted that, in a clean system, the electrons would take on the form of concentric rings. These rings, according to Landau, increase according to their energy level. The new study validates Landau's theory. This counting behavior forms the basis of the so-called Hall Effect.

The Hall Effect is seen when a magnetic field is applied perpendicular to the flow of electrical current. The field causes resistance in the current that pushes negatively charged electrons, resulting in a weak but measurable voltage, perpendicular to both the current flow and the applied magnetic field.

In recent years, this effect has been used to define the standard for what we mean by electrical resistance and could soon be employed to define the kilogram.

Professor Rudolf Roemer of the Department of Physics at the University of Warwick said, “This is an exciting step for us, we are really seeing for the first time individual quantum mechanical wave functions of electrons in real materials. On the face of it this might seem far removed from everyday life."

“However the question of what defines a kilogram is currently being debated, with the spacing between the rings of these Landau levels acting as a kind of marker for a universal weight. So next time you measure out your sugar to bake a cake, you might unknowingly be making use of these quantum rings.”

The results of this new study were published in the journal Physical Review Letters.