deletions | additions       diff --git a/section_GaN_Bandstructure_Sze_simplifies__.tex b/section_GaN_Bandstructure_Sze_simplifies__.tex  index cf64d8a..d55ff08 100644  --- a/section_GaN_Bandstructure_Sze_simplifies__.tex  +++ b/section_GaN_Bandstructure_Sze_simplifies__.tex 
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\section{GaN Bandstructure}  Sze simplifies the problem by using a parabola with curvature set by the effective mass for the dispersion, but one really should use the material-appropriate imaginary bandstructure in the gap, as shown in \ref{fig:imagBS}. In order have a usable form for the bandstructure, I've taken the 4x4 $k\cdot p$ Hamiltonian from \cite{Rinke_2008}, and specified it to the $\hat{z}$ direction, which removes most of the off-diagonal matrix elements. In fact, along the $z$-axis, the Hamiltonian can be reduced to an effective two-band model (similar to but more general than (Kane_1960). \cite{Kane_1960}.  \[  H=\begin{pmatrix}  E_g'+\frac{\hbar^2k_z^2}{2m_e} & iP_1k_z\\