Recent content by Kirjava

Let me address a possible misconception first: the correspondence between AZ symmetry classes and the classifying spaces is "dimension dependant", so it doesn't quite make sense to equate R_4 with the symmetry class AII. Regarding your question: you're right that a PH symmetry is not present...

Hi Comrade, I'm glad to see that this (rather old) discussion is still proving useful to somebody. I started this thread whilst I was (beginning) to write my undergraduate thesis on the subject of topological insulators and their K-theory classification - out of curiosity may I presume to ask...

Of all the references I find Dunne's approach on page 52 of http://arxiv.org/pdf/hep-th/9902115v1.pdf the most understandable. He shows exactly how the Chern-Simons term arises through an explicit computation and obtains its coefficient. Unfortunately these computations are carried out for Dirac...

Hi PF, I'm still very much a novice when it comes to QFT, but there's a particular calculation I'd like to understand and which (I suspect) may be just within reach. In short, the result is that after coupling a system of fermions to an external U(1) gauge field, one obtains a Chern-Simons...

To clarify, is the Hall current shared between bulk and edge states in such a way as to preserve its precise quantization?

Hi PF, Hoping somebody out there can help me to clear up what is probably a silly misunderstanding of the IQHE: Since the quantized Hall current can be expressed as a property of occupied bulk bands (Chern number) why do we say that the current is carried by the edge states?

Thanks for the attentive replies as usual. I understand that once interactions are added things become less clear, and there are (many?) known interacting cases where the BBC fails. Nevertheless I think it's still an interesting question to ask whether it holds in all the known non-trivial...

There appear to be a number of different approaches to characterizing the bulk of a topological insulator (some of which may avoid this difficulty), but the simplest non-interacting methods are formulated in the language of Bloch wavefunctions and Hamiltonian. An edge or interface obviously...

In the literature on topological insulators and superconductors the 'bulk-boundary correspondence' features quite heavily. One version of this conjecture says roughly: "At an interface between two materials belonging to the same symmetry class with bulk invariants n and m, precisely |n-m|...

I've been wondering about where this connection would lie along the axis of profundity, but figured that I wouldn't find out until I got around to studying it in detail. Hmm. Thanks for the references again. I've also been entertaining the possibility of investigating the status of Kitaev's work...

Hi element4, thanks for the links. Regarding sources for KR-theory, I've found that a combination of Kitaev's primary reference (the book by Max Karoubi) and the original paper by Atiyah (e.g. www.maths.ed.ac.uk/~aar/papers/atiyahkr.pdf) is fairly comprehensive. Karoubi develops ordinary...

That time dilation, how does it work? In seriousness though, Personally I've found many of the more 'physical arguments' in this area to be quite baffling. Again, they presume a certain amount of familiarity and intuition for concepts that I just don't have. The mathematical arguments...

Thanks again Monkey, some resolution on these issues comes as quite a relief (unfortunately nobody in my department studies these things, so they'd been bottled and stewing for quite a while). Rather than harassing you with endless questions though, could I ask you to recommend a text which...

Another less speculative question if anyone is still out there: I've seen a few authors talk about creation/annihilation operators as though they're automatically defined globally over the whole Brillouin zone (e.g. Equation 12 of the paper Monkey linked). Doesn't this amount to assuming that...

Ah, I meant to say " ... written in terms of quadratic combinations of Majorana operators", so your second point was really the one I was after. Sorry about that. It seems to me that if we relax the restriction to quadratic hamiltonians the "real structure" of his K-theory classification is...