refractive index of graphene

[NW]

Hi,

I used GGA and HSE06 to calculate refractive index of graphene. The results show approximately n=1.7 for visible light range. In this reference [https://aip.scitation.org/doi/10.1063/1.3475393] n has been calculated experimentally and it was equal around 3. I attached my scripts here.
Is there any parameter that should be changed?

Thanks

[NW]

Hello,

I still need help to figure out how to obtain the correct value of refractive index for graphene.

Thanks

[Anders Blom]

With the latest version of QuantumATK 2019.12 you can also include the intraband contributions - since graphene is kind of metallic, that may actually help. See https://docs.quantumatk.com/manual/Types/OpticalSpectrum/OpticalSpectrum.html#intraband-contribution

Otherwise it looks to me that you have chosen appropriate settings in your script, except perhaps the bands above and below the Fermi level. It's hard to guess these, but you should increase them and check if that has any influence on the results (and the same goes for the k-points, but 100 points seems reasonable).

Now, generally when asking for our assistance, it's very hard to judge anything from your results just being given a single number. You need to study carefully the entire dielectric function, real and imaginary part, for the whole spectrum, and compare that to other results, incl. bulk C to check the accuracy of the method you are using. . And very importantly, given that graphene is so anisotropic, you will at least get two results for parallel and perpendicular polarization. I checked the literature very quickly and the number 1.5 seems quite reasonable, actually for one of the polarizations. See e.g.
https://ieeexplore.ieee.org/document/8354508
https://doi.org/10.1016/j.physe.2014.04.010
https://doi.org/10.1016/j.jpcs.2017.06.026

Btw, I doubt HSE and GGA will yield significantly different results, esp. since there is no band gap, thus I would focus my energy on GGA to save time.

Good luck, I hope something here helped you!

[Petr Khomyakov]

I used GGA and HSE06 to calculate refractive index of graphene. The results show approximately n=1.7 for visible light range.

Given that periodic boundary conditions are imposed in all 3 space directions, did you check how GGA-calculated refractive index value depends on the vacuum thickness in-between graphene monolayers in neighboring cells in out-of-plane C-direction? Now it is set to 12 Ang in the script. What would happen if it is 24 Ang, for instance?

[NW]

Dear Petr,

I tested the vacuum level in z direction effect on refractive index and the results were so sensitive to this parameter. What is the reason behind it? and how can I choose the accurate vacuum level in this case?

Thanks

[Petr Khomyakov]

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?