# Illustration Energy Spectrum vs. Chemical Potential in a Kitaev Chain

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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 $$\mu \approx 2$$.