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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 $\partial_\mu\equiv \frac{\partial}{\partial k_\mu}$, ...

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To respond directly regarding the Materials Project data, I'm a staff member there so maybe I can shed some light. Materials Project computed data is currently generated using a technique known as Density Functional Theory (DFT) with the PBE exchange-correlation functional. This results in some well-understood, systematic differences from experiment. ...

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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=... 10 I will give a quick answer from my experience, but typically you want to use the computed lattice parameter. The reason for this is that otherwise you induce strain in your computed cell, but in general this is a red flag anyways. You really want your computed lattice parameter to match if possible which might involve using a different functional or even ... 9 Actually, if you allow for quasi-2D systems, graphene has had a recent renaissance starting with the experimental discovery of correlated states in "magic angle" twisted bilayer graphene, which was originally predicted by Bistritzer and MacDonald. By stacking two graphene layers with a relative twist, new structures with very long periodicity can ... 9 From the available information, I think it is caused by the small value of T_{damp}. This causes the T to fluctuate wildly, which can induce unwanted bond-breaking. Best practise is to keep T_{damp} value around 100 \times \text{timestep}. Also, I will suggest you use a much larger neighbour bin size (\approx 3 Å ). 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 ... 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 I have to disagree with the answer of @Tristan. The x-ray diffraction, both powder and single crystal, has enough precision and quality (equipment and software) to give very good and real experimental values. It is well known that very few DFT approximations (methods, functional, pseudopotential, basis set, etc.) give good lattice values. And when we said ... 6 I believe what you are referring to is a "projected" or "fat" band structure diagram. By assigning colors (or line thickness) to a basis on which you project the Kohn-Sham states (pseudoatomic orbitals, Wannier functions, etc.) you can plot the band structure in a way that shows the composition of all the states in the bands in terms of ... 6 You generally cannot calculate a 2D system per se with a plane-wave program, but rather you should do a vacuum slab calculation. As for graphene, you would essentially do a calculation on graphite, but with the interlayer distance set at a large value, say 20 Angstrom (and the lattice constant c enlarged accordingly), so that the different layers of graphene ... 6 I am not aware of any reason (and don't see) why VASP is more popular than its contemporaries for 2D materials. VASP does have some features that other packages don't, but it also has its own drawbacks. You can refer to this discussion where differences between the two most common packages (VASP and Quantum ESPRESSO) are outlined. In general, I have come ... 5 Not a direct answer to your question, but I hope you will still find this relevant. A very useful online tool to construct Brillouin zones and conventional \mathbf{k}-paths for structures of any symmetry is SeeK-path. Inputs. It accepts input structures in the formats from major DFT codes (Quantum Espresso, Castep, Vasp), as well as other formats like cif, ... 5 I didn't notice this before, but the link provided in the question can already be used to visualize any 2D Brillouin zone. Since you can define the ratio of b/a, and the angle between b and a, then you can define any 2D Bravais lattice. There are only 5 possibilities. The "hexagonal" and "square" options are just there to conveniently show two of them. The ... 5 You can safely use a dispersion corrected DFT method for 2D systems if your vacuum space is large enough, but there is another issue that must be explained. Most of the current dispersion correction methods such as DFT-D(Grimmes D2/D3/D4), TS, MBD, etch methods are overestimating interlayer interaction, exfoliation energies. They are not safe to use if you ... 4 The VASP package solving the KS-equation with periodic boundary conditions (PBC). For two-dimensional materials such as graphene, you only have two periodic directions along \vec{a} and \vec{b} but the VASP assumes you still have three directions. To avoid this, you need to add enough vacuum (in general large than 15 angstroms) along the \vec{c} ... 3 The main idea here is to preserve the periodic boundary conditions when creating a fractional supercell. Therefore, not all combinations are possible, such as \sqrt{2}\times\sqrt{2} or\sqrt{5}\times\sqrt{5} for the case of MoS_2. Basically, you need to define a rotation matrix for creating such supercells. e.g., B=RA (in matrix form), where A is the ... 3 As a good starting, you may take a look at this classical paper and its supplementary material: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.117.097601 Here I just show some general steps: Calculate the polarization (I assume that you can use the VASP package): Calculate the A, B, C, D of Landau-Ginzburg expansion:$$E= \sum_i \dfrac{A}{2}(...

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Technically I'm not answering your question of whether this method is applicable to slabs of ~3 nm thickness, but wanted to give you an answer that could be helpful anyway. I would not generally use '2D' for slabs, although I have not tested it before. The parameter of interest here is assume_isolated = 'esm'. In my own experience, with ESM vs. a standard ...

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