Related seminar tomorrow https://researchseminars.org/talk/BeijingMoscowColloquium/11

Mathematical problems in the theory of topological insulators

Armen Sergeev (Steklov Mathematical Institute of RAS)

*Abstract*: The talk is devoted to the theory of topological insulators - a new and actively developing direction in solid state physics. To find a new topological object one have to look for the appropiate topological invariants and systems for which these invariants are non-trivial. The topological insulators are characterized by having wide energy gap stable for small deformations. A nice example is given by the **quantum Hall spin insulator**. It is a two-dimensional insulator invariant under the time reversal. It is characterized by the non-trivial topological -invariant introduced by Kane and Mele. In our talk we consider the topological insulators invariant under time reversal. In the first part we present the physical basics of their theory while the second part deals with the mathematical aspects. These aspects are closely related to K-theory and non-commutative geometry.

Yeah, that kind of information could be what the entry needs. I am doing some edits at the moment. Maybe you can do more afterwards.

We don’t need to resolve other people’s debates, but we need to have a minimum of sanity in the text of our entries lest the $\mathbb Zn$Lab looks silly. It should go without saying that an entry needs attention when it essentially consists of a single reference whose only commentary says that it’s irrelevant.

]]>One could also consult the 2007 paper on the experimental discovery

]]>Konig, M.; Wiedmann, S.; Brune, C.; Roth, A.; Buhmann, H.; Molenkamp, L. W.; Qi, X.-L.; Zhang, S.-C. (2007)

Quantum spin Hall insulator state in HgTe quantum wells, Science, 318(5851), 766–770 doi:10.1126/science.1148047

Urs, I am sorry but I did and do not feel competent to resolve this complaint (beyond leaving both the reference and the complaint) regarding that it is apparently clash between too big external authorities on the significance and interpretation of Bernevig, Hughes and Zhang 2006. which has been entered by me on the basis of external authorities (including wikipedia) rather than my own judgement.

Namely, the wikipedia article on Shoucheng Zhang and National Academy of Sciences quote there claim that that reference 10 in comprehensive wikipedia article provide the discovery of topological insulator and quantum spin Hall.

The 2018 Zhang obituary in Nature says

in 2006 Zhang and his co-authors predicted the existence of a

topological insulator(B. A. Bernevig et al. Science 314, 1757–1761; 2006), which led to an experimental study the following year (on which he collaborated) that achieved the first observation of such an insulator in nature (M. Koenig et al. Science 318, 766–770; 2007). The topological insulator had near-perfect conduction at its surface edges thanks to a phenomenon called thequantum spin Hall effect.

(underlined by Z. Š.)

The same reference Bernevig et al. is taken as basic in the main article wikipedia/Topological insulator as well, along with quoting Kane and Mele 2005. We may also compare similar statement in wikipedia/Quantum spin Hall_effect quoting the same reference along with Kane and Mele (and Haldane for prehistory, of course).

I would like to help, I do believe that Prof. Wen has a good theoretical reason to believe that something is wrong with this quote but I can hardly ignore wikipedia and Nature sources. It seems you are now more interested in that subject (when I added the reference we had a guest at my institute talking about the stuff and after some conversations I decided to make some stubs to kick off, but my readings did not grow in later years.)

I can now ask one of my colleagues who is a world leading expert in spintronics for his opinion though, but it will take few days to get the response.

]]>Just to highlight that in rev 2, from Oct. 2013 Xiao-Gang Wen added a remark claiming that the single reference given here is no good.

Wen added the analogous comment to *topological insulator* in rev 5, from Oct 2013

(I haven’t looked into it yet, just highlighting the edit for the moment, which seems to have gone unnoticed.)

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