This is a question about deriving effective mass theory for graphene. For the two sub-lattice atoms, the wave equation can be written as the massless Dirac equation:
$ \displaystyle -i\hbar v_F \begin{pmatrix} 0 & \partial_x -i\partial_y \\\partial_x +i\partial_y & 0 \end{pmatrix} \left(\begin{array}{c} \Psi_A \\ \Psi_B \end{array}\right)=E \left(\begin{array}{c} \Psi_A \\ \Psi_B \end{array}\right) \ \ \ \ \ (1)$ where ${A,B}$ are two subatoms.
The derivation of the equation went back to 1984, which is the paper I am trying to understand. In the article, they argued that at first order of ${\vec{\kappa}\cdot \vec{p}}$ expansion, the momentum matrix can be written in the form, under group-theoretic arguments (equation (3) in the paper):
$ \displaystyle \bar{p}\begin{pmatrix} 0 & \hat{x} -i\hat{y} \\ \hat{x} +i\hat{y} & 0 \end{pmatrix} . \ \ \ \ \ (2)$
What is the argument behind it? Is there anyone read the paper or know the answer?
