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3

First of all, H-phase TMDC monolayers like $\ce{WSe_2}$ are non-magnetic semiconducting materials, which means the time-reversal symmetry (TRS) is preserved. Therefore, you can say the energy states at $K$ and $-K$ are connected by TRS, seeing this post. For H-phase TMDC monolayers, the inversion symmetry (IS) is broken. In addition, the spin-orbit coupling ...

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I found the following slides helpful: https://physics.princeton.edu//~haldane/talks/dirac.pdf Here are my answers: Yes. From what I understood, the above is not necessarily a 3D effect. The wormholes appear only at gapless points, so we can expect only one Dirac string in my example. Partly correct. We have only one wormhole from the gapless point. However, ...

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I don't think I can use this Hamiltonian to recover the band structure. The band structure should use a tight-binding Hamiltonian with several unit cells. A colleague told me that this Hamiltonian is just for their discussion in Figure 4.

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The TD-Schrodinger equation is $$H(\lambda)|\psi(t)\rangle=i\hbar\frac{\partial}{\partial t}|\psi(t)\rangle$$ So, we just need to plug in \eqref{4} and remove all terms that aren't first-order in $\dot\lambda$. Let's start with the left-hand side, since its a little simpler. \begin{align}H(\lambda)|\psi(t)\rangle&=e^{i\phi(\lambda(t))}e^{-i\gamma(t)}\...

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