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Messages - Petr Khomyakov

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Regarding computing DOS for graphene see Appendix in Phys. Rev. B 87, 075414 – Published 7 February 2013. As Tue suggested also try increasing the number of k-points significantly. Did you also use tetrahedron method with significantly increased k-point density? It would also be helpful to see your script.

This is exactly what my previous post is about that one can define the physical position of the Fermi level when using the Fermi Dirac broadening method available in QuantumATK for DFT calculations for a given electronic temperature, which acts a broadening/smearing parameter in SCF electronic structure calculations, see the manual for more details.

If one uses the Fermi-Dirac smearing (not MP or others) for an SCF calculation, the position of the Fermi level is physical, and one can then see whether a semiconductor is intrinsic or doped by looking at the CBM or VBM position with respect to the Fermi level.

The unit cell of graphene should be rectangular to make it possible to attach electrodes.

It can be the same if degeneracy of all the bands is the same.

Quantum capacitance is in general defined in terms of density of states: For multiple-band case as yours, you would have to sum up DOS defined for each band separately. So, I guess if defined in terms of group velocities, it would be something like sum over inverse velocities corresponding to the bands that are crossed by the Fermi level. For each band, one should also account for state/band degeneracy essentially given by N_ch in the capacitance formula in the "reference" paper.

The best way to see whether your system has a band gap or not is to compute density of states. For graphene, you should use really many k-points to sample the Brillouin zone (for band structure and dos calculation) properly around the conical point, see Appnedix in Phys. Rev. B 87, 075414 – Published 7 February 2013. Note that one may have a band gap in some directions even for metallic systems, e.g., check the Fermi surface of bulk copper, which has a hole in one of the k-directions, even so copper is definitely a metal.

I was proposing an asymmetric k-grid because your original ribbon was defined roughly as a 3x1 rectangular cell. If you now use a nearly-square unit cell then it makes sense to adopt a symmetric k-grid. Typically, for a given crystal structure one chooses k-lines in-between k-symmetry points in the Brillouin zone, but then you have to set your unit cell type (Bravais lattice explicitly to allow QuantumATK to set them automatically). For a square lattice, G-X, Y, G is a natural route. So, just use a lot of k-point to eliminate the energy gap, which does not exist in pristine graphene, and in your calculations resulted from a coarse k-point sampling.

Did you check if increasing the k-point sampling resolves the issue?

k_point_sampling = MonkhorstPackGrid(

Try using something like nb=12, nc=36 for the nanosheet system, instead of the coarse and highly-asymmetric k-grid, nb=3, nc=3, as set in the current script.

The configuration has a rather small interlayer separation distance in C-direction, set it to 20 Ang, for example. The same separation distance should then be used for the nanosheet structure. Note that you have it in A-direction for the nanosheet, unlike the graphene sheet structure.

For the nanosheet, you may use, e.g., G, Z, G, Y, Z k-path. In the current definitions, G-Y is along the nanosheet, whereas G-Z is perpendicular to that. 

In principle, the electronic structure of graphene should not depend on the choice of its unit cell. Of course, the band structure plot will look somehow different because the Brilloiun zone depends on the unit cell choice, meaning that bands will be folded when going from the primitive cell of graphene to some unit cells. But these are still the same bands. So, no band gap should be seen in any band structure of pristine graphene.

I have also notice that you have used really few k-points  for SCF calculations, so I would suggest increasing it until convergence for total energy and band structure convergence is achieved, i.e., these 2 quantities do not virtually change when you further increase k-point sampling.

Please clarify what is the total velocity.  I believe the problem is not on the usage of velocity function, but on the problem formulation and choice of the actual approach for quantum capacitance calculations. It would be helpful to see a reference to the theory behind what you are trying to do.

Which version of QuantumATK are you using? Also, please attach your python script and related log file.

Please attach your python script and related log file.

The choice totally depends on what you want to do with these velocities, i.e., it is your choice that probably depends on the research problem you are trying to solve.

Questions and Answers / Re: refractive index of graphene
« on: May 13, 2020, 09:40 »
The reason I believe is that the optical spectrum analysis object relies on the Kubo-Greenwood formula for dielectric function, which allows calculating optical response for a given 3D material, i.e., a material infinite in all three spatial directions. There is then a well-established relation between the dielectric function and refractive index, so that the latter can be computed.

The actual question is what is the meaning or definition of the dielectric function and related refractive index for a 2D material that is one atom thick.  Treating it as a 3D system with a given vacuum thickness means that most of this graphene monolayer + vacuum system has refractive index of 1 (refractive index of vacuum), and the vacuum contribution will increase when enlarging the vacuum thickness.

How do you define dielectric function / refractive index of a graphene monolayer?

Questions and Answers / Re: GaAs(110)_surface
« on: May 12, 2020, 02:08 »
Please attach a script for the figure you have posted.

Keep in mind that in the Cleave Tool there exist two options of choosing a termination plane and also set the in-plane lattice vectors. Using these two options, you must be also create any surface of InAs, provided that all the surface atoms in that paper are kept at their bulk InAs sites, i.e., not moved manually. If moved, you may then use Move Tool in the Builder to manipulate surface atoms after cleaving a surface.

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