Course Report: Solid State Physics in Three Classes

In the last course report post, we dispensed of atomic and molecular physics in just three classes. The next three classes do the same for solid state physics.

Class 25 picks up on the idea of basic molecular potentials from the end of the previous class, and uses that to introduce energy bands in a qualitative manner. Bringing two atoms together splits the electron levels into two states, adding a third adds more closely spaced levels, and so on. Every time you add more atoms, you add more closely spaced energy levels, and as you approach truly macroscopic systems, those states run together into energy bands.

Then, I talk about this a little more formally, in the Kronig-Penney model of a periodic array of square wells. We don't go through all the math in gory detail, but we did talk about the square well potential, as well as barrier penetration and tunneling. They've seen the boundary value matching problem in those contexts, so they can at least understand the set-up of the problem.

I show them the transcendental equation that results from the Kronig-Penney model, and then how that leads to bands of allowed states. Having thus established the existence of energy bands twice, I close with a short explanation of how band structure explains electrical conductivity.

Class 26 picks up on band structure, and talks about semiconductors and semiconductor doping. I explain how you can make p-type and n-type semiconductors by adding different impurities to silicon, and how this lets you control the conductivity of the semiconductor. then I go into how a p-n junction lets you make a diode, which allows current to flow in only one direction. Then there's a very quick and qualitative explanation of how transistors work.

Class 27 moves on to talk about superconductivity. I show a sketch of the original superconductivity data from Onnes, and then talk about possible ways this might come about. I give a hand-wavy explanation of how lattice vibrations lead to increased resistance (basically a Drude-type model of ballistic electron motion, with ion cores sometimes moving into the path of an electron). This leads to decreasing resistance at low temperature, but won't get you to zero resistance, because of zero-point energy.

Then I digress a little to talk about distribution functions, and how the Fermi-Dirac distribution leads to electrons at very high energies. I then show the Bose-Einstein distribution as an alternative, and talk a bit about superfluidity, which is a frictionless flow of atoms related to Bose-Einstein Condensation. If we could somehow make a BEC of electrons, we might be able to explain superconductivity.

This is followed by a hand-wavy discussion of Cooper pairing, in which electrons can "pair up" through interactions mediated by the positive ions in the lattice. These electron pairs have two spin-1/2 particles, making them a composite boson, which can then Bose condense. This can only happen if the vibrational motion of the ions is small enough that to be overcome by interactions with the electrons, which is why it's a very low temperature phenomenon.

The discussion of superconductivity is mostly an excuse to break out the liquid nitrogen and show them the Meissner effect in high-T_c superconductors, levitating a little magnet over a chunk of ceramic superconductor. And then to play with the liquid nitrogen a bit because, dude, liquid nitrogen!

If the previous post's material was a mess, textbook-wise, this is even worse. From memory, I think this starts in Chapter 8, then skips to Chapter 11, drops back into Chapter 10, then briefly into Chapter 9, and finishes up in Chapter 10. Again, though, it's as clear a narrative flow I can construct from this collection of topics.