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Currently, I am repeating the results of this famous paper written by Di Xiao. In this paper, the authors construct a minimal band model based symmetry arguments and $\vec{k}\cdot\vec{p}$ method. The final Hamiltonian is $$\hat{H} = at(\tau k_x \hat{\sigma}_x+k_y\hat{\sigma}_y)+\dfrac{\Delta}{2}\hat{\sigma}_z-\lambda \tau \dfrac{\hat{\sigma}_z-1}{2}\hat{s}_z .$$

For completeness, the following screenshot describes the procedure which the author stated in his paper.

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The following is the known fact based on first-principles calculations. enter image description here

My question is about how to construct such a Hamiltonian? What's the general workflow?

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  • $\begingroup$ You are basically asking for a course in band structure calculations, no? $\endgroup$ – Jon Custer Aug 28 '18 at 14:27

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