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16

The Berry curvature is defined as: $$\Omega_{\mu\nu}(\mathbf{k})=\partial_{\mu}A_{\nu}(\mathbf{k})-\partial_{\nu}A_{\mu}(\mathbf{k}), \tag{1}$$ where $A_{\mu}(\mathbf{k})=\langle u_{\mathbf{k}}|i\partial_{\mu}u_{\mathbf{k}}\rangle$ is the Berry connection, $|u_{\mathbf{k}}\rangle$ is a Bloch state, and $\partial_\mu\equiv \frac{\partial}{\partial k_\mu}$, ...

12

Resolution for the time reversal symmetry: I need to demonstrate: $\Omega(-\mathbf{k})=-\Omega(\mathbf{k})$ (Berry's curvature is a odd function under time reversal symmetry) Berry's curvature: $$\Omega_{\mu\nu}(\mathbf{k})=\partial_{\mu}A_{\nu}(\mathbf{k})-\partial_{\nu}A_{\mu}(\mathbf{k})\tag{1}$$ If the system is time-reversally invariant: T|u_k\rangle=...

6

I should start by saying that I am no expert in MoS$_2$, so this answer is my guess from looking at the reference you provide, and would be happy if someone corrects me. The general things to keep in mind when looking at such band structures are: If the system has time reversal symmetry, then if there is an electron with quantum numbers $(\mathbf{k},\... 4 Whenever I hear spintronics, valleytronics, twistronics or anything that really breaks down to the study of quantum transport, I always think of the people who taught me Quantum Mechanics and work in this field and a code called kwant. While I do not study these topics myself, I used to try to learn related topics and I took a couple workshops since I was ... 3 First of all, H-phase TMDC monolayers like$\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$are connected by TRS, seeing this post. For H-phase TMDC monolayers, the inversion symmetry (IS) is broken. In addition, the spin-orbit coupling ... 2 ProfM's argument is absolutely right. Here I support a more detailed explanation based on first-principles calculations. The spin-resolved band structure of monolayer MoS$_2$with the consideration of spin-orbit coupling is shown below: You can first find the two split valence bands around$K$and$-K$valleys. In particular, spin-$z\$ is a good quantum ...

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