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I'm confused about majorana modes at the edge of Kitaev chain, what do we seek in experiment? When we first define this one we write the creation and annihilation operators as: $$a^{+}=\frac{1}{2}(\gamma_{1}+i\gamma_{2}),\ a=\frac{1}{2}(\gamma_{1}-i\gamma_{2})$$ Condensed matter systems are made out of electrons, and these always correspond to pairs of Majoranas. But in topological phase we have unpaired Majoranas at the edge of chain, it seems this is only math trick. We can find either an electrone or a hole and nothing more.

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The point is there is a zero-energy occupied state. So for instance in conductivity experiments one looks for a zero-bias peak. I don't think it's been completely settled. See eg. https://arxiv.org/abs/1706.07033

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