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I Why and how Dirac cones are "tilted"?

  1. Aug 1, 2017 #1
    Given a Weyl Hamiltonian, at rest,

    \begin{align}
    H = \vec \sigma \cdot \vec{p}
    \end{align}

    A Lorentz boost in the x-direction returns

    \begin{align}
    H = \vec\sigma\cdot\vec{p} - \gamma\sigma_0 p_x
    \end{align}

    The second term gives rise to a tilt in the "light" cone of graphene. My doubts are:

    How I can derive such term given a Lorentz transformations in x direction? If the cone of "light" is "tilted" then the Fermi velocity has changed?


    [Tilted anisotropic Dirac cones in quinoid-type graphene and α−(BEDT-TTF)2I3][1]



    gX0SF.jpg
     
  2. jcsd
  3. Aug 6, 2017 #2
    Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
     
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