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I am putting together a presentation on topological phase transitions in 1D tight binding models for a course in Solid State Physics, and while I have found many sources for theoretical descriptions I have not found many experimental sources. I am particularly interested in the Su-Schrieffer-Heeger (SSH) model for polyacetylene, although I know the Kitaev chain is somewhat more well known.

Specifically, I want to know: have the zero-energy edge modes predicted by the SSH model been observed, either in polyacetylene or in another related system? How about for the Kitaev chain? Are there any other experiments that have confirmed predictions from these models?

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  • $\begingroup$ Take a look at this paper: arxiv.org/abs/1607.02811 $\endgroup$
    – Rococo
    Commented Dec 10, 2016 at 19:26
  • $\begingroup$ I think in 1D polymers the answer is no, there has not been a direct observation of such edge modes. $\endgroup$
    – KF Gauss
    Commented Aug 12, 2018 at 20:12

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I'm not so familiar with SSH model, but as mentioned in comments, there are experiments with ultracold atom that have proven the existence of the soliton state.

For Kitaev chain, Majorana zero mode has been reported experimentally since 2012, see arXiv: 1204.2792. The group in Delft has discovered zero modes at the edges of spin-orbit coupled semiconductor chain in the vicinity of s-wave superconductor.

But it is not a conclusive result, since there are other possibilities of obtaining zero modes. Thus there are many groups trying to find other evidence such as the non-Abelian braiding statistics, etc.

It wouldn't be so distant before groups find some smoking gun evidence, I suppose.

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For Kitaev chain, Majorana zero mode has been reported experimentally since 2012, arXiv: 1204.2792.

Mourik and Frolov, co-authors of the mentioned paper, admit here (2022) that "key smoking gun evidence of Majorana is still lacking".

This blogpost by Douglas Natelson provides some useful context.

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  • $\begingroup$ You can probably find a more convincing source than an April Fool's arXiv paper. They have both been vocal over the last couple of years (particularly Frolov, in my experience) that they do not consider the reported Majorana "discoveries" sufficiently supported. $\endgroup$
    – Anyon
    Commented Jun 30, 2023 at 14:04
  • $\begingroup$ @Anyon I know. That's what they they state in the above paper too. It's April 12, btw. $\endgroup$ Commented Jun 30, 2023 at 16:33
  • $\begingroup$ I frankly have no idea where you got "April 12" from, but you do you. $\endgroup$
    – Anyon
    Commented Jul 1, 2023 at 15:35
  • $\begingroup$ @Anyon You are right, I got mixed up. Still, the paper's abstract contains a recent explicit statement that evidence of Majorana is still lacking, which is the point. The flawed-data-selection argument is as relevant as ever. $\endgroup$ Commented Jul 2, 2023 at 4:51

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