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Illustration Probability Density of Majorana Fermions in a Kitaev Chain (Graph)

Probability Density of Majorana Fermions in a Kitaev Chain (Graph)
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Probability densities \(|\psi_0|^2\) and \(|\psi_1|^2\) of Majorana fermions (Majorana zero modes) in a Kitaev chain described by the following Hamiltonian:$$ H ~=~ -\mathrm{i}w \, \underset{j}{\boxed{+}}~ c_{2j}\,c_{2j+1} $$

Here, \(c_{2j}\) and \(c_{2j+1} \) are Majorana operators applied to the same \(j\)-th site in a Kitaev chain. The hopping parameter \(w=2\) and the pair potential \(\mathit{\Delta}=2\) were chosen for the plot. The chemical potential is \(\mu=0\) and the number of fermionic sites is \(N=30\). Each fermionic site can be occupied by two Majorana fermions.

As can be seen from the diagram, the Majorana fermions (with the energies equal to zero) are most likely to be found at the edges of the Kitaev chain.