## Tuesday, April 15, 2014

### 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