Illustration Energy Spectrum vs. Chemical Potential in a Kitaev Chain

The energy spectrum \(W_n\) as a function of the parameter \(\mu / w \) (\(\mu\): chemical potential, \(w\): Hopping parameter) for the following Hamiltonian function:\begin{align} H_1 ~&=~ -\underset{j}{\boxed{+}}~ \mu \, c_{2j-1}\,c_{2j} \\\\ ~&+~ \underset{j}{\boxed{+}}~ \left(w+|\Delta|\right)c_{2j}\,c_{2j+1} \end{align}

Here, \(c_{2j-1}\), \(c_{2j} \) and \(c_{2j+1} \) are Majorana operators applied to the \(j\)th site in a Kitaev chain. For the plot, the hopping parameter \(w=2\) and the pair potential \(\mathit{\Delta}=2\) were chosen.

Two Majorana fermions are created at the edges of the Kitaev chain and each has energy \(W = 0 \). The Majorana fermions, as seen on the plot, remain stable up to \(\mu \approx 2\).