Ciro Santilli @cirosantilli 37

As mentioned on the introduction, the main objective of the course is to try predict qualitative properties of materials, notably the existence of certain phase transitions, starting from first principle toy models.

Key phenomena covered include:

An alloy of iron and carbon. Because such allys have had such incredible historical importance due to their different properties, different phases of Fe-C have well known names such as steel

If you adda bit of impurities to certain materials, at low temperatures of a few Kelvin their resistivity actually starts increasing if you go below a certain critical temperature.

For Fractional quantum Hall effect for $\nu =1/m$.

We know that superfluidity happens more easily in bosons, and so electrons joins in Cooper pairs to form bosons, making a superfluid of Cooper pairs!

Isn't that awesome!

Bibliography:

In some contexts, we want to observe what happens for a given fixed magnetic field strength on a specific plate (thus $t$ and $n$ are also fixed).

In those cases, it can be useful to talk about the "Hall resistance" defined as:So note that it is not a "regular resistance", it just has the same dimensions, and is more usefully understood as a proportionality constant for the voltage given an input $I_x$ current:

This notion can be useful because everything else being equal, if we increase the current $I_x$, then $V_y$ also increases proportionally, making this a way to talk about the voltage in a current independent manner.

And this is particularly the case for the quantum Hall effect, where $R_{xy}$ is constant for wide ranges of applied magnetic field and TODO presumably the height $t$ can be made to a single molecular layer with chemical vapor deposition of the like, and if therefore fixed.