Friday, June 6, 2014

Brillouin Zones, Band Gaps, Bloch Oscillations, the Electron-Hole Asymmetry Theory of Superconductivity

I'm reading through the following in preparation for writing a (hopefully) simplified summary of the electron-hole theory of superconductivity.  For those who would like to follow along, each of the references below i a great resource targeted at different experience levels.

1.   +Jonah Miller's article on band structure as it relates to how materials conduct electric charge[1].  This is a great starting point for the lay-audience.  Jonah is great at explaining physics at any level by the way!  He recently walked Elaine and I through the rudiments of lattice gravity calculations over alcoholic slushies at the +APS Physics April meeting.

Photo Credit +Jonah Miller 

2.  Dr. Likharev's, (of Stony Brook University), Quantum Mechanics I notes relating to the same topic, but from the point of view of Bloch's theorem.  These are targeted at the physics graduate student reader.  His notes show how the unallowed regions in Jonah's article are predicted mathematically; there are no real valued solutions for the quasi-momentum of the charge carrier in the gap.  Dr. Likharev points out some useful derivation starting points, such as using periodic delta functions as a simple model for a crystalline lattice.  He also points out an interesting interpretation of holes.  Mathematically they look like electrons whose effective mass is negative.  This will come in handy later when Hirsch discusses holes un-dressing to become electrons.

3.  Finally, my own article discussing the superconductor band gap video from the '60s.  While I made fun of educational videos like this when I was in school, this on has significantly augmented my understanding of what band structures really mean.  Alfred Leitner rocks!

For those of you who missed the video the first time, here it is again

1.  Jonah Miller on Bandgaps

2.  Dr. Likharev's notes

3.  My article regarding the superoncductor energy gap

4.  Alfred Leitner's instructional video about the superconducting energy gap

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