Tuesday, May 14, 2013

Thoughts on Fairbank's Quantized Flux Discovery and the Quantum Hall Effect

William Fairbank might be most famous for experimentally demonstrating that magnetic flux is quantized[1].  In 1961 he published the results of an experiment that exposed very small cylinders of superconducting tin to a magnetic field and then measured the magnetic flux trapped by the cylinder after the applied magnetic field was turned off.  For more detail on why the flux was trapped, see [2].  He arrived at the following graph of trapped flux vs. applied field strength. (picture 1)



The data points are clustered around magnetic flux levels on the y axis that correspond to the values predicted for the magnitude of quantized magnetic flux.  The apparatus for the experiment is similar in several ways to the apparatus for the fractional charge experiment I mentioned yesterday [3].  A superconductor was exposed to an external magnetic field and results were analyzed by measuring properties of an induced vibration of the superconductor through a magnetometer, (an inductive pickup coil).

Almost three decades later in 1980, Klitzing experimentally verified the quantum Hall effect.  This is another effect due to the quantitization of magnetic flux.  His data was similar to the following[4].  Notice the naturally similar structure, (both experiments are measuring quanta of magnetic flux). (picture 2)

A few years later in 1997, it was experimentally verified that in a two dimensional electron gas, electrons could behave as quasi-particles with one third the charge of a normal electron.  The following data shows a plateau at a flux level corresponding to a charge of 1/3[5]. (picture 3)


My leisure time this week is probably going to wind up being spent wondering if the fractional quantum hall effect had anything to do with the fractional charge results Fairbank reported in 1977[3].  Does anyone happen to know if this has ever been addressed?  All thoughts, comments, and/or questions are always welcome!

A final note, Fairbank's constructed his quantized flux apparatus based on a vibrational magnetometer design published in 1959[7].  It's definitely my favorite piece of experimental equipment for the week.  The prototype was build from a loudspeaker, a drinking straw and a paper cup! (picture 4)



References:
1.  
http://dx.doi.org/10.1103%2FPhysRevLett.7.43
Deaver B. & Fairbank W. (1961). Experimental Evidence for Quantized Flux in Superconducting Cylinders, Physical Review Letters, 7 (2) 43-46. DOI:

2.  Flux trapping on Copasetic Flows

3.  Fairbank and fractional charge

4.  Quantum Hall review article
http://dx.doi.org/10.1103%2FRevModPhys.59.781
Yennie D. (1987). Integral quantum Hall effect for nonspecialists, Reviews of Modern Physics, 59 (3) 781-824. DOI:

5.  Fractional quantum Hall effect (open access)
http://rmp.aps.org/abstract/RMP/v71/i4/p875_1

6.  Scientific American on the Quantum Hall Effect
http://ist-socrates.berkeley.edu/~phylabs/adv/ReprintsPDF/SHE%20Reprints/21-Quantized%20Effect.pdf

7.  Fairbank apparatus progenitor
http://dx.doi.org/10.1063%2F1.1716679
Foner S. (1959). Versatile and Sensitive Vibrating-Sample Magnetometer, Review of Scientific Instruments, 30 (7) 548. DOI:

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