Skip to main content

Superconductors, the London Moment, and Spin Currents

In addition to the Meissner effect pictured to the left, superconductors have other odd properties.  One of them is something known as the London moment.  It's named after the London brothers who did some of the earliest work on the properties of superconductors.  If I had to take a guess, I'd say it was specifically named after  Fritz London who authored the two volume set of books, "Superfluids"[1].  So much for the naming of the thing, here's what happens.  When a superconductor is rotated, it produces a magnetic field aligned with the axis of rotation.  The magnetic field is linearly related to the angular velocity of the superconductor by the following equation, (picture 2)[2].



where m_e is the mass of the electron, c is the speed of light, and e is the charge of an electron.

London theorized that the  magnetic field which bears his name was a result of the superconducting cooper pairs lagging behind the initial rotation of the superconductor bulk.  Thereafter, they never quite catch up and there's a relative current between the superconducting electrons and the body of the superconductor.  It's this current he reasoned that is responsible for the magnetic field.

Dr. Jorge Hirsch of UCSD has posited a different mechanism for the production of the London moment in his paper titled "Spin currents in superconductors[2]".  Hirsch theorizes that the current responsible for the London  moment is not due to the lag of superconducting electrons spinning up and trying to catch  up with the rest of the superconductor, but instead is due to counterposed currents of electrons whose spins are opposite to one another travelling around the surface of the superconductor.  The currents come in pairs.  A current of spin up electrons moving in the clockwise direction around a superconductor is always accompanied by a current of spin down electrons moving in the opposite direction.  In this way, in equilibrium, there is no detectable charge or spin currents since each pair of counter-spinning counter-traversing currents effectively cancels each other out.  According to Hirsch, these hypothetical counterposed spin currents are setup in the superconducting material when it enters the superconducting state.  A diagram of two pairs of the spin currents in a spherical superconductor is shown in picture 3[2].


Hirsch presents a very nice macroscopic explanation of how the spin currents create the London moment currents when the superconductor is rotated.  At the most basic level, the London moment current due to the spin currents compensates for the extra centripetal force on the superconducting electrons.  I'll have to leave that for another time though.

References:
1.  London's book on superconductors
http://books.google.com/books?id=mNwLMwEACAAJ&dq=superfluids+fritz+london+volume+1+dover&source=gbs_navlinks_s

2.  Hirsch's paper on superconductors and spin currents (open access)
http://arxiv.org/abs/cond-mat/0406489


Labels:

Comments

Post a Comment

Please leave your comments on this topic:

Popular posts from this blog

The Valentine's Day Magnetic Monopole

There's an assymetry to the form of the two Maxwell's equations shown in picture 1.  While the divergence of the electric field is proportional to the electric charge density at a given point, the divergence of the magnetic field is equal to zero.  This is typically explained in the following way.  While we know that electrons, the fundamental electric charge carriers exist, evidence seems to indicate that magnetic monopoles, the particles that would carry magnetic 'charge', either don't exist, or, the energies required to create them are so high that they are exceedingly rare.  That doesn't stop us from looking for them though! Keeping with the theme of Fairbank[1] and his academic progeny over the semester break, today's post is about the discovery of a magnetic monopole candidate event by one of the Fairbank's graduate students, Blas Cabrera[2].  Cabrera was utilizing a loop type of magnetic monopole detector.  Its operation is in...
1 comment
Read more

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

Now available as a Kindle ebook for 99 cents ! Get a spiffy ebook, and fund more physics 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 ...
11 comments
Read more

More Cowbell! Record Production using Google Forms and Charts

First, the what : This article shows how to embed a new Google Form into any web page. To demonstrate ths, a chart and form that allow blog readers to control the recording levels of each instrument in Blue Oyster Cult's "(Don't Fear) The Reaper" is used. HTML code from the Google version of the form included on this page is shown and the parts that need to be modified are highlighted. Next, the why : Google recently released an e-mail form feature that allows users of Google Documents to create an e-mail a form that automatically places each user's input into an associated spreadsheet. As it turns out, with a little bit of work, the forms that are created by Google Docs can be embedded into any web page. Now, The Goods: Click on the instrument you want turned up, click the submit button and then refresh the page. Through the magic of Google Forms as soon as you click on submit and refresh this web page, the data chart will update immediately. Turn up the:...
Post a Comment
Read more