deletions | additions       diff --git a/In_the_same_manner_we__.tex b/In_the_same_manner_we__.tex  index f1b0d21..c908920 100644  --- a/In_the_same_manner_we__.tex  +++ b/In_the_same_manner_we__.tex 
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\begin{equation}  h(k_{x},h_{y})=\begin{pmatrix} Asink_x \\ Asink_y \\ \Delta+cos(k_{x})+cos(k_{y}) \\ \end{pmatrix}  \end{equation}  The Chern number of the system can be thought as a monopole at the $\textbf{h}$ space origin. And as $k_x$ and $k_y$ go from $-\pi$ to $\pi$ ,which corresponds to the 1st Brillouin zone, it is a torus walking in the $h$ $\textbf{h}$  space. As long as the torus passing through origin, it contributes 1 Chern number. The evolution of the torus is shown in Fig.8. The $\Delta$ parameter controls the initial center of the torus. Therefore, different $\Delta$ values determines different topological order of the system.