Skip to main content

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)

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
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)

6.  Scientific American on the Quantum Hall Effect

7.  Fairbank apparatus progenitor
Foner S. (1959). Versatile and Sensitive Vibrating-Sample Magnetometer, Review of Scientific Instruments, 30 (7) 548. DOI:


Popular posts from this blog

Cool Math Tricks: Deriving the Divergence, (Del or Nabla) into New (Cylindrical) Coordinate Systems

The following is a pretty lengthy procedure, but converting the divergence, (nabla, del) operator between coordinate systems comes up pretty often. While there are tables for converting between common coordinate systems, there seem to be fewer explanations of the procedure for deriving the conversion, so here goes!

What do we actually want?

To convert the Cartesian nabla

to the nabla for another coordinate system, say… cylindrical coordinates.

What we’ll need:

1. The Cartesian Nabla:

2. A set of equations relating the Cartesian coordinates to cylindrical coordinates:

3. A set of equations relating the Cartesian basis vectors to the basis vectors of the new coordinate system:

How to do it:

Use the chain rule for differentiation to convert the derivatives with respect to the Cartesian variables to derivatives with respect to the cylindrical variables.

The chain rule can be used to convert a differential operator in terms of one variable into a series of differential operators in terms of othe…

Lost Phone

We were incredibly lucky to have both been in university settings when our kids were born.  When No. 1 arrived, we were both still grad students.  Not long after No. 2 arrived, (about 10 days to be exact), mom-person defended her dissertation and gained the appellation prependage Dr. 

While there are lots of perks attendant to grad school, not the least of them phenomenal health insurance, that’s not the one that’s come to mind for me just now.  The one I’m most grateful for at the moment with respect to our kids was the opportunities for sheer independence.  Most days, we’d meet for lunch on the quad of whatever university we were hanging out at at the time, (physics research requires a bit of travel), to eat lunch.  During those lunches, the kids could crawl, toddle, or jog off into the distance.  There were no roads, and therefore no cars.  And, I realize now with a certain wistful bliss I had no knowledge of at the time, there were also very few people at hand that new what a baby…

Lab Book 2014_07_10 More NaI Characterization

Summary: Much more plunking around with the NaI detector and sources today.  A Pb shield was built to eliminate cosmic ray muons as well as potassium 40 radiation from the concreted building.  The spectra are much cleaner, but still don't have the count rates or distinctive peaks that are expected.
New to the experiment?  Scroll to the bottom to see background and get caught up.
Lab Book Threshold for the QVT is currently set at -1.49 volts.  Remember to divide this by 100 to get the actual threshold voltage. A new spectrum recording the lines of all three sources, Cs 137, Co 60, and Sr 90, was started at approximately 10:55. Took data for about an hour.
Started the Cs 137 only spectrum at about 11:55 AM

Here’s the no-source background from yesterday
In comparison, here’s the 3 source spectrum from this morning.

The three source spectrum shows peak structure not exhibited by the background alone. I forgot to take scope pictures of the Cs137 run. I do however, have the printout, and…