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Kevin Lee edited textbf_Edge_States_Now_we__.tex
over 8 years ago
Commit id: f4453b2a07c5a29d12cbc31d66cdecbdd445ff33
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\textbf{Edge States:} Now we consider a special case of hBHZ model. We break the 2D lattice into a strip, which means the lattice is still translational invariant along x-direction. However, the y-direction has finite number of atoms. We can modified the previous Hamiltonian in this way.
\begin{equation}
\textit{H({k_x})}=\sum_{y=1}^{N}[\Delta+cosk_{x}]\sigma_z+Asink_x\sigma_x]\bigotimes \textit{H(k_x)}=\sum_{y=1}^{N}[\Delta+cosk_{x}]\sigma_z+Asink_x\sigma_x]\bigotimes |y\rangle\langle y|+\frac{1}{2}\sum_{y=1}^{N-1}(\sigma_z-iA\sigma_y)\bigotimes|y+1\rangle \langle y|+(\sigma_z+iA\sigma_y)\bigotimes|y\rangle \langle y+1|
\end{equation}