In the past few days I've become increasingly intrigued by the QHE, mainly thanks to very interesting questions and answers that have appeared here. Unfortunately, I am as of yet very confused by all the (seemingly disparate) stuff I learned.
First, here are some random points that I've been able to gather
- I(nteger)QHE occurs due to the presence of Landau levels
- IQHE is an embodiment of topological order and the states are characterized by the Chern number that tells us about topologically inequivalent Hamiltonians defined on the Brillouin zone
- IQHE requires negligible electron-electron interations and so is dependent on the presence of impurities that shield from Coulomb force
- F(ractional)QHE occurs because of formation of anyons. In this case Coulomb interaction can't be neglected but it turns out an effective non-interacting description emerges with particles obeying parastatistics and having fractional charge
- FQHE has again something to do with topology, TQFT, Chern-Simons theory, braiding groups and lots of other stuff
- FQHE has something to do with hierarchy states
So, here are the questions
- Most importantly, do these points make sense? Please correct any mistakes I made and/or fill in other important observations
- How do explanations 1. and 2. of IQHE come together? Landau quantization only talks about electron states while topological picture doesn't mention them at all (they should be replaced by global topological states that are stable w.r.t. perturbations)
- How do explanations 4., 5. and 6. relate together
- Is there any accessible introductory literature into these matters?
- Do IQHE and FQHE have anything (besides last three letters) in common so that e.g. IQHE can be treated as a special case? My understanding (based on 3.) is that this is not the case but several points hint into opposite direction. That's also why I ask about both QHE in a single question