deletions | additions       diff --git a/In_the_manner_we_can__.tex b/In_the_manner_we_can__.tex  index be43d71..0df2440 100644  --- a/In_the_manner_we_can__.tex  +++ b/In_the_manner_we_can__.tex 
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In the manner, we can visualize the problem in the $h(k_x,k_y)$ form. We can rewrite the spectrum in the following way.  \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 $h$ 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 $h$ space. As long as the torus passing through origin, it contributes 1 Chern number.