16

Two-band model for graphene. To simplify the discussion of Dirac points, it is sufficient to consider a nearest-neighbor tight-binding 2-band model for graphene. This is a spinless model because spin-orbit is negligible in graphene. The Bloch Hamiltonian is: $$ \hat{H}(\mathbf{k})= \begin{pmatrix} 0 & h(\mathbf{k}) \\ h^{\dagger}(\mathbf{k}) & 0 \end{...


14

The reason why graphene has Dirac points at K and $-$K is because of a combination of time reversal and inversion symmetries. Therefore, if you impose these symmetries in your VASP calculation, there is no reason why there should be a gap at K. Even if you do not impose these symmetries explicitly, you should be able to get the degeneracy to very high ...


10

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 $).


9

Oh! I found the answer already. Since I'm doing the calculation along the High symmetry point. Im doing the calculation along G -> K -> M -> G, that's why the right hand sides show such phenomena. In tight binding I plot the band along G -> K -> G. I try to reproduce the band along this direction, it matched with the tight binding solution. Thanks guys. It's ...


9

The $\Sigma$ values represent the volume of the Coincident Site Lattice (CSL) of the grain boundary in terms of the volume of the unit cell of the crystal. In general, grain boundaries with higher symmetry have lower $\Sigma$ values. Note that CSL boundaries are special grain boundaries. So, they do not represent all grain boundaries comprehensively. But, ...


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

As mentioned by @Camps in the comments, the Zn reference used in the paper is almost certainly that of an isolated Zn atom in the gas phase. If I understand correctly from briefly scanning the paper, the source of Zn in the device (as viewed from the graphene-coated separator) will be Zn2+ ions dissolved in the electrolyte - not quite the same thing as Zn in ...


4

This Physics Stack Exchange thread answers this question very well. Apparently, the length scale of such "logarithmic divergence" is actually merely in the order of atomic distances even if the entire graphene sheet is as large as the solar system! So practically, the results of the theorem is irrelevant to the real-world graphene, even though ...


3

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.


3

There has indeed been quite a lot of research in this area, as is readily uncovered by searching for "improving the strength of graphene" in your search engine of choice; for example, this 2017 review https://www.sciencedirect.com/science/article/pii/S0079642517300968. Graphene is often highlighted as having high mechanical strength, but this ...


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