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P wave superconductivity

  1. Feb 3, 2017 #1
    Hello! So I'm really stuck in a personal quest to derive Kitaev's 1D p wave superconductivity model, and I'm stuck on the seemingly simplest part.

    1. The problem statement, all variables and given/known data

    In the Bogluibov transformation, we get two coefficients from the equations

    [itex] |v_{k}|^{2}+ |u_{k}|^{2}= 1 [/itex]

    [itex] v_{k}=(\frac{E_{Bulk}-\epsilon_{k}}{\Delta_{k}})\mu_{k} [/itex]

    Where [itex] E_{Bulk} = \sqrt{\epsilon_{k}^{2} + |\Delta_{k}|^{2}} [/itex]

    3. The attempt at a solution

    I cannot derive the correct expression for [itex]u_{k} [/itex]

    [itex] u_{k} = \frac{\Delta_{k}}{|\Delta_{k}|}\frac{\sqrt{E_{Bulk}+\epsilon_{k}}}{\sqrt{2E_{Bulk}}} [/itex]

    I know it's just simple algebra, but I've been working on it for hours without any progress and I can't find any sources online that show the derivation :O
  2. jcsd
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