Graphene Equation LaTeX Source

\documentclass[aps,12pt,prb]{revtex4}

\begin{document}

\title{Graphene Susceptibility}

\author{R. B. Laughlin}

\affiliation{Stanford}

\date{17 May 08}

\maketitle

Density of states.

\begin{displaymath}
{\cal D}(E) = - \frac{1}{\pi} \lim_{\eta \rightarrow 0} {\rm Im}
\biggl\{ \sum_\lambda \frac{1}{\Omega_{BZ}} \int_{BZ}
\frac{dq_x dq_y}{E - E_q^\lambda + i \eta} \biggr\}
= \sum_\lambda \frac{1}{\Omega_{BZ}} \int_{BZ}
\delta(E - E_q^\lambda) \; dq_x dq_y
\end{displaymath}

Sum rule:

\begin{displaymath}
\int_{-\infty}^\infty {\cal D}(E) \; dE = \sum_\lambda 1 = 2
\end{displaymath}

\begin{displaymath}
E_q + \Delta {\bf q} \cdot \nabla_q E_q = E_\pm
\end{displaymath}

\end{document}