deletions | additions       diff --git a/The_integer_QHE_has_a__.tex b/The_integer_QHE_has_a__.tex  index 27a9040..b95adbd 100644  --- a/The_integer_QHE_has_a__.tex  +++ b/The_integer_QHE_has_a__.tex 
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\begin{equation}  b_z(k)=i(\langle\partial_x{u_k}|\partial_y{u_k}\rangle-\langle\partial_y{u_k}|\partial_x{u_k}\rangle)  \end{equation}  The $b_z(k)$ is so called Berry curvature. When we apply the electric field in the y-axis, we have $\dot(k_y)\sim-\frac{eE_y}{\hbar}$. Therefore, the hall conductivity can be approximated as $\sigma_{xy}\sim{b_z(k)}$ $\sigma_{xy}\sim{b_z(k)}$.