The Quantum Hall Effect |
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| The
quantum Hall effect (QHE),
discovered in 1980 by K. v.
Klitzing et. al., [Phys.
Rev. Lett. 45, 494-497 (1980)] is, in essence, a remarkable manifestation
of quantum mechanics on a macroscopic scale. Instead of the usual Hall
effect, the dramatic features of the QHE are clearly seen in the figure
above, where we plot Rxx, the resistance in the current direction, and Rxy
(right hand Y-axis), the 'resistance' perpendicular to the current flow,
as a function of the applied magnetic field, B. Of the many aspects that
appear in these traces, the most prominent is, of course, the strict quantization
of Rxy at certain values of B. The plateau marked by n=2
is exceptionally impressive and we are unable to detect, within our measurement
capabilities, deviations from quantization at a value of resistance Rxy=h/2e^2,
where h is Plank's constant and e is the elementary charge. The state-of-the-art
methods for estimating these deviations result is an upper bound of 4 parts
in 10^10. This constitute the most accurate measure of the h/e^2 ratio.
This quantization is so precise, that the QHE is now used as the world standard
for defining the Ohm!
Although we sometimes use
the best quality materials that can be obtained, to me the most remarkable
fact about the QHE is that it is a direct consequence of disorder. In
fact, it is well established that in the absence of disorder the QHE would
not be resolved. The QHE is the prominent system where quantum physics
shows its beautiful face only as a result of disorder. |
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