# Tag Info

16

I have seen all the methods you mentioned but have only done one myself; I'll explain here how to use Wannier90 in conjunction with Quantum Espresso to get band structures for hybrid functional calculations. It does take a bit of time to learn, but not very long! You can learn the basics and do some first calculations in an afternoon. There are subtleties of ...

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=...

9

What is the quantum anomalous Hall effect? Figure from C-X. Liu, S-C. Zhang, and X-L. Qi. "The Quantum Anomalous Hall Effect: Theory and Experiment," Annual Review of Condensed Matter Physics 7, 301-321 (2016) (arXiv link). In short, the quantum anomalous Hall effect (QAHE) is the quantized version of the regular anomalous Hall effect (AHE). That ...

9

This has already been asked in several forms in Physics Stack Exchange. Within the semi-classical 'electric dipole' approximation, only the electric field of light interacts with the electron. The effect of magnetic field is usually very weak except for a few cases like highly concentrated pulses etc. Magnetic field can flip spins, in a process called 'spin-...

8

Quantum confinement can occur when the exciton (electron-hole quasiparticle) radius is larger than the size of the semiconductor. Due to this confinement, the energy levels which can be occupied by the exciton are quantized into discrete energy levels. This will spread the band gap due to missing states that would exist in the bulk material. This ...

8

Let's give it another go: In the monolayer you would place the inversion centre on the green atom. But this would reverse the direction of the trigonal prism formed by the yellow atoms. Hence, there can't be an inversion centre. In the bilayer the inversion centre is between the layers. Then the direction of the trigonal prism is reversed but it is also ...

7

How do you get the Hamiltonian formula for transition metal dichalcogenides? How to derivate the expression above (equation (1))? You can use the $k \cdot p$ method to derive this effective Hamiltonian. Please take a look at this paper for the details. $k \cdot p$ theory for two-dimensional transition metal dichalcogenide semiconductors. What does the ...

7

Apart from methods (1) and (2) mentioned in the question, the third method I found to be pretty viable under certain conditions. The procedure involves mathematical interpolation of the bands, so I have to caution the reader that this is not completely rigorous like Wannier interpolation, which retains the nature of the wave-functions generated from the SCF ...

6

I don't think there is a consensus of norm conserving PP being more accurate. There are some references I am aware of which have calculated dielectric tensor using NC-PP, but without justification though: Yu, E. K.; Stewart, D. A.; Tiwari, S. Ab Initio Study of Polarizability and Induced Charge Densities in Multilayer Graphene Films. Phys. Rev. B - Condens. ...

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 $(\mathbf{k},\... 6 well, you certainly can change the spin of an electron through acting on its orbital motion with the electric field. It is called "spin-orbit coupling" (SOC) and a lot of magneto-optical and opto-magnetic (inverse) effects completely rely on it. You might want to look at papers discussing all-optical magnetization switching with circularly ... 5 I think the claim assumes linear polarization of the light which has zero angular momentum. For circularly polarized light, the spin of the electron should be flipped. (e.g. Appl. Phys. Lett. 114, 041104 (2019)) Indeed, it has a probability issue as explained by @Xivi76. 4 Quantum confinement is a kind of physical effect, which describes the change of electronic and optical properties when the material sampled is of sufficiently small size----typically 10 nanometers or less. For layered TMDC materials, when the materials are downsized to the 2D limit, the dielectric screening environment will be reduced significantly, and ... 4 As @Jack suggested, try the$\vec{k} \cdot \vec{p}$method. The hopping integral$t_{ij}$is "borrowed" from the Hubbard model. It is the kinetic term in the Hamiltonian that explains electrons being able to "hop" from one atomic site to another. In real space, it is an integral of the orbital overlap between the two neighboring atomic ... 3 First of all, H-phase TMDC monolayers like$\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$are connected by TRS, seeing this post. For H-phase TMDC monolayers, the inversion symmetry (IS) is broken. In addition, the spin-orbit coupling ... 3 DFT-D2 is simple and reliable. I've used DFT-D2 for most of my worked on 2D materials but I do I have to caution you that I have not specifically work on TMGs. You can test out the results you obtain from both DFT-D2 and DFT-D3 and compare them. Another idea is to look at literature. There is a labyrinth of data on TMGs and you can look under the 'methods' ... 2 ProfM's argument is absolutely right. Here I support a more detailed explanation based on first-principles calculations. The spin-resolved band structure of monolayer MoS$_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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