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

References:
1. Jonah Miller on Bandgaps
http://www.thephysicsmill.com/2013/02/03/im-with-the-valence-band-band-structure-and-the-science-of-conduction/

2. Dr. Likharev's notes
https://drive.google.com/file/d/0B30APQ2sxrAYaXE0MG1FRWxVcDg/edit?usp=sharing

3. My article regarding the superoncductor energy gap
http://copaseticflow.blogspot.com/search?q=superconductor+band

4. Alfred Leitner's instructional video about the superconducting energy gap
http://youtu.be/1KuxdKGm3V4

Comments

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...

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 ...

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:...

Copasetic Flow

Search This Blog