Thursday, May 29, 2014

The Superconductor Hole-Electron Asymmetry of Hirsch

What follows is an explanation of a phrase that Hirsch uses in most of his papers, “hole-electron asymmetry of condensed matter”.  The explanation was adapted from one of Hirsch’s papers[1], that can be found on arxiv as well as Phys. Rev . B.
Hirsch frequently refers to the ‘hole-electron asymmetry of condensed matter’.  In the article entitled “Electron-hole asymmetry and superconductivity”, he provides a nice picture of exactly what he means by this phrase.  I adapted the explanation for a presentation I’ll give soon on the H-ray theory.  The slides follow.  A more complete and texty explanation can be found at the link above.  The text that follows below is the very rough draft of some of the vernacular for the presentation.  For those who are die-hard fans of watching people fumble with practice presentations, I've also posted the first run-through of these slides.  The video is more for my reference than anything else.  You’ve been warned :)

In Hirsch’s papers, he talks a lot about something he calls the hole-electron asymmetry of condensed matter and he has one paper where he actually describes in a pretty nice way what he means by the hole-electron asymmetry of condensed matter.  Normally when you’re doing condensed matter physics you can talk about electrons, (negatively charged particles), or holes.  Holes are taken by al lot of people to mean a lack of an electron so it means a positive charge where an electron would have been and they talk about them fairly symmetrically.  So, for example, they’d say that an electron current moving to the righ in this picture is the same as a hole current moving to the left.  Almost all their equations work out great because when you change the sign of the charge on the charge carrier, you also change the sign of the velocity, and so things like the sign of the current stay the same.  This is what Hirsch describes as symmetry.   You can’t tell l the difference between holes and electrons in a lot of condensed matter physics.

When you get to superconductors, this is where Hirsch points out the hole electron asymmetry.  In superconductors, there are experiments that show that the charge carriers have to be electrons and can’t be holes.  One of them is the London moment.  In that experiment, the physically rotate a superconductor, like our superconducting cylinder here, and a magnetic field is created that points (actually down) into the superconductor if it’s rotating in a counter-clockwise direction.    That field points down because the charge carriers that create the field are electrons, negative charge carriers.  If the charge carriers were holes, they would be positive and the magnetic field would point in the opposite direction.  So, what Hirsch means when he says the hole-electron asymmetry in condensed matter physics is that in superconducting materials, there are experiments where you can tell that the current involved is a current of electrons and not a current of holes moving in the opposite direction.  The reason we believe it’s electrons is that the electrons are moving along with the superconducting cylinder, (lagging just a bit), and when the electrons rotate this way they create a magnetic field that is anti-parallel to the angular velocity vector, which is what we see.

1.  Hirsch, J. E ., ”Electron-hole asymmetry and superconductivity”, Phys. Rev. B, **68**, (2003),

2.  My complete derivation of the London penetration depth from the London field and a few other notes in LaTex.  Thanks to the folks at +writeLaTeX for making everything so easy!

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