CrazyNeutrino said:
Physicists Net Fractal Butterfly
http://www.scientificamerican.com/article.cfm?id=physicists-net-fractal-butterfly
After a nearly 40-year chase, physicists have found experimental proof for one of the first fractal patterns known to quantum physics: the Hofstadter butterfly. Named after Douglas Hofstadter, the Pulitzer prizewinning author of the 1979 book Gödel, Escher, Bach, the pattern describes the behavior of electrons in extreme magnetic fields.
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Electrons under the influence of a magnetic field would race around in circles. But Hofstadter found that in theory, if the electrons were confined inside a crystalline atomic lattice, their motion would become complicated. As the magnetic field was cranked up, the energy levels that define the motion of electrons would split again and again. When represented on a graph, those energy levels revealed a pattern that looked like a butterfly — and continued to do so, even when zoomed in to infinitely small scales.
The idea was difficult to test. The strength of the required magnetic field depends on the spacing between the atoms in the lattice. In conventional materials, in which atoms are separated by less than one-billionth of a metre, the pattern can emerge only in fields on the order of tens of thousands of tesla. The best available magnets can reach only about 100 tesla, and for just a fraction of a second.
But smaller fields are sufficient in lattices with larger spacings, which can be created by layering materials in stacks. In May, researchers reported that they had stacked a single sheet of graphene, in which carbon atoms are arranged like a honeycomb, on top of a sheet of honeycombed boron nitride. The layers create a repeating pattern that provides a larger target for magnetic fields than the hexagons in each material — effectively magnifying the field.
After applying a field, the researchers measured discrete changes in the conductivity of the composite material — stepwise jumps that result from splits in the energy levels of its electrons. These were not a direct detection of the expected electron behavior, but were a proxy for it.