deletions | additions       diff --git a/With_some_derivations_we_can__.tex b/With_some_derivations_we_can__.tex  index 6a86163..9d9ec6d 100644  --- a/With_some_derivations_we_can__.tex  +++ b/With_some_derivations_we_can__.tex 
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Now we expand our discussions to 2 dimensional lattice called "Berevig Hughes Zhang Model". It can be used to describe the most common topological insulator HgTe quantum well system. Now we consider the half BHZ model instead of the full version. Its Hamiltonian can be written down as  \begin{equation}  \textit{H(k)}=[\Delta+cos\textit{k}_x+cos\textit{k}_y]\sigma+A(sin\textit{k}_x\sigma_x+sin\textit{k}_y\sigma_y)  \end{equation} The term $\Delta$ is just like a Zeeman splitting term. The $A$ is the spin-orbit coupling term. The last term in the equation describes a hopping with spin flips. With the Hamiltonian, we can calculate the energy dispersion. The results are in Fig.7