deletions | additions       diff --git a/begin_equation_sigma__xy_v__.tex b/begin_equation_sigma__xy_v__.tex  index 95372fe..10bc632 100644  --- a/begin_equation_sigma__xy_v__.tex  +++ b/begin_equation_sigma__xy_v__.tex 
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This "$v$" number is called TKNN number or Chern number. Now we know that the conductivity is proportional to Chern number. And it can be proven that each occupied Landaul level contributes to one Chern number. The energy eigenvalue of Landaul level is of the form  \begin{equation}  \epsilon_n=(n+\frac{1}{2})\hbar\omega_c  \end{equation} where $\omega_c=\frac{eB}{m}$.