Explain the integer quantum Hall effect
The integer quantum Hall effect is a remarkable manifestation of quantum mechanics in a two-dimensional electron system. When such a system, typically an inversion layer in a semiconductor, is cooled to very low temperatures and exposed to a strong perpendicular magnetic field, the Hall resistance, R_H, exhibits plateaus. On these plateaus, R_H is precisely quantized to values h/(i*e^2), where 'h' is Planck's constant, 'e' is the elementary charge, and 'i' is an integer. This quantization is so exact that it becomes a standard for resistance. It arises from the formation of Landau levels in the electron system, and the integer 'i' relates to the number of filled Landau levels, a concept deeply connected to topology.
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