# I Why and how Dirac cones are "tilted"?

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1. Aug 1, 2017

### devmessias

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]

2. Aug 6, 2017

### PF_Help_Bot

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