If you've ever wanted to learn about the quantum hall effect, this is your chance. A lecture note on this very topic is now available online, all 102 pages of it!
Abstract: These lecture notes yield an introduction to quantum Hall effects both for non-relativistic electrons in conventional 2D electron gases (such as in semiconductor heterostructures) and relativistic electrons in graphene. After a brief historical overview in chapter 1, we discuss in detail the kinetic-energy quantisation of non-relativistic and the relativistic electrons in a strong magnetic field (chapter 2). Chapter 3 is devoted to the transport characteristics of the integer quantum Hall effect, and the basic aspects of the fractional quantum Hall effect are described in chapter 4. In chapter 5, we briefly discuss several multicomponent quantum Hall systems, namely the quantum Hall ferromagnetism, bilayer systems and graphene that may be viewed as a four-component system.
I've skimmed through the first few pages (yeah, like I have the time to read through carefully the whole thing...), and it looks quite good, especially if you're an advanced physics undergraduate or a graduate student. The first few pages alone will tell you why the study of quantum hall effect is so important and very fundamental that it transcends beyond condensed matter physics.
Zz.
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