deletions | additions       diff --git a/begin_equation_sigma__xy_v__.tex b/begin_equation_sigma__xy_v__.tex  index 8e102a4..c0e9a42 100644  --- a/begin_equation_sigma__xy_v__.tex  +++ b/begin_equation_sigma__xy_v__.tex 
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\begin{equation}  \epsilon_n=(n+\frac{1}{2})\hbar\omega_c  \end{equation}  where $\omega_c=\frac{eB}{m}$. We are ready to explain why increasing B would increase the conductivity(or reduce the resistivity). When we increase the B field, the separation between each Landaul level starts to increase. And the system's Fermi energy does not change. Therefore, as the B increases, the total number of occupied Landual levels decreases. Then the conductivity decreases( or resistivity increases as Fig.1). The complete derivation is in \cite{Takahashi_2015} \cite{Takahashi_2015}.