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Can someone explain the fractional quantum Hall effect in layman's terms, I'm having some difficulty understanding it?

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marked as duplicate by yuggib, ACuriousMind, John Rennie, Martin, LDC3 Jun 10 '15 at 2:25

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Imagine you have a tower standing in a lake. The walls of the tower are permeable to water, so the height of the water inside the tower matches the height of the water outside of the tower. We can adjust the height of the water in the lake. Our objective is to determine the number of floors that have their surface area covered by water.

If, as we adjust the height of the water, we find that there is always an integer number of floors covered in water, we would assume that each floor is flat. However, if as we adjust the height of the water we find that floors can be partially covered in water, we'd conclude that each floor was bumpy, or irregular, such that sections of each floor could be below water while other sections could be above water.

Now let's make an analogy. The water is a reservoir of electrons. The height of the water is the chemical potential of the reservoir of electrons. The tower is our system (2D sheet of metal) connected to the reservoir. The floors of the tower are the Landau levels. The partially covered floors of the tower represent the fractionally filled Landau levels. The phenomenon of fractional filling gives us insight into the structure of each Landau level.

I'm not quite sure how to finish the analogy to connect this to the fractionally quantized Hall resistance. Please feel free to add below.

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