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For a $p_x+ip_y$ superconductor, at its boundary there will be an edge state $$ \gamma_{p} = \alpha_pc_p + \alpha_{-p}^*c_{-p}^\dagger, $$ where $c_p$ is an ordinary fermion operator and $p$ denotes the momentum. It has chirality with the dispersion relation $E_p = v_Fp$ and satisfies the relation $\gamma_{p}^\dagger = \gamma_{-p}$.

This edge state is usually called as a chiral Majorana fermion. However, a Majorana fermion must equal to its Hermitian $\gamma^\dagger = \gamma$ in my understanding.

Why $\gamma_p$ is considered or called as a Majorana fermion here?

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  • $\begingroup$ $\gamma(x)^\dagger=\gamma(x)\Rightarrow\gamma(p)^\dagger=\gamma(-p)$... $\endgroup$
    – AccidentalFourierTransform
    Commented Nov 30, 2022 at 13:59
  • $\begingroup$ So people call $\gamma(p)$ a Majorana fermion because $\gamma(x) = \int dp e^{ip x} \gamma(p)$ is a Majorana fermion. So is there an original paper mention it ? Just curious about it. $\endgroup$
    – lsdragon
    Commented Dec 1, 2022 at 2:51

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