2D material optical properties

[muhammadhasan]

Hi,

When we calculate epsilon (dielectric function) using yambo (IP RPA) for 2D material (e.g graphene, MoS2), Do we need to consider any factor for multiplication with the result printed in yambo?
For example, in the Quantum ESPRESSO Course for Solid-State Physics(https://doi.org/10.1201/9781003290964) book, they mention that:

Note: For the 2D material, we must reduce the value of Re(ε(ω)) and Im(ε(ω)) by a dimensionless c/L, where c is the height of the unit cell including the vacuum region and L is the real thickness of the 2D material. For the monolayer MoS2, c is 20 Å in scf.in and L = 6.5 Å is given by the experiment

so, in yambo, for 2D material, do we need any special care like this (since using Quantum Espresso we already taking special care, for example, adding vacuum gap to cut attraction between the sheet)?

Best
M J Hasan
PhD Student
Mechanical Engineering
University of Maine

[Daniele Varsano]

Dear M J Hasan,

2D material in Yambo are treated by adding vacuum in the supercell and using a truncated coulomb cutoff potential.
The dielectric function printed by Yambo in this case is not meaningful as it tends to the limit o vacuum Re(eps)=1, Im(eps)=0, and the quantity to be analysed is the polarizability (alpha). No additional factors need to be taken into account.

Best,

Daniele

[muhammadhasan]

Hi Professor,

Thank you for your comments. Actually, in my research I need to solve a radiation transmission function between two materials (2D/3D) separated by vacuum, and that function is basically a inverse dielectric function of several q vectors (using IP RPA) Considering the fact,
1) Is it possible that, for 2D materials, we will find out polarizability (alpha) using Yambo, and then convert it to dielectric function using mathematical formulae? After that, the dielectric will be using in my research?

2) How about 3D case, Can we use the dielectric function directly which is printed in yambo?


Thank you so much.

Best
M J Hasan
PhD student
Mechanical Engineering
University of Maine

[Daniele Varsano]

Dear M J Hasan,


1) You can find here relations between polarizability and dielectric function can be found e.g. here:
PHYSICAL REVIEW B 84, 085406 (2011), Eq. 16 (note that eps is defined in 3D).
See also Eq. 6 for definition of eps_2D.

2) Yes, in a 3D system the eps is well-defined, and it is reported in the yambo output.

Best,

Daniele

[muhammadhasan]

Hi Professor,

Thank you for your comments. Usually, I use the command 'yambo -o c' to prepare the input file (IP-RPA) and it prints o-*.eps and o-*eels. To print the result of polarizability(alpha), would you please suggest me which command I have to add there?

Thank you

Best
M J Hasan
PhD student
Mechanical Engineering
University of Maine

[muhammadhasan]

Hi Professor,

Might be I got my answer of the previous question. I have seen that if I use "yambo -coulomb -optics c" this command, it prints alpha as well as eps and eels. I have some questions regarding that:

Code: Select all

RandQpts=1000000                       # [RIM] Number of random q-points in the BZ
RandGvec= 100                RL    # [RIM] Coulomb interaction RS components
CUTGeo= "slab z"                   # [CUT] Coulomb Cutoff geometry: box/cylinder/sphere/ws/slab X/Y/Z/XY..
% CUTBox
 0.000000 | 0.000000 | 0.000000 |        # [CUT] [au] Box sides
%
CUTRadius= 0.000000              # [CUT] [au] Sphere/Cylinder radius
CUTCylLen= 0.000000              # [CUT] [au] Cylinder length
CUTwsGvec= 0.700000              # [CUT] WS cutoff: number of G to be modified

1) I have used "slab z" here. As in DFT, I used vacuum (e.g, graphene) in the z direction (vertical), x and y direction is equivalent. For other parameters such as RandQpts, CUTGeo, I have used that value by following an example online. so do I need to convergence test for those parameters? and I kept untouched the parameters such as CUTRadius, CUTCylLen and CUTwsGvec.

2) Equation 6 of your referred paper is "epsilon(q)=1+2*pi*alpha*|q|". However, in the case of q = (0, 0, 0), epsilon(q) is 1. So, Is it okay, professor? or for epsilon at q =0, I should use the epsilon value printed in yambo directly. As I notice at |q|=0, the Re(eps) is not close to 1 (its around 8).

3) Is the unit of alpha printed in yambo in "atomic unit (a.u)" ?

Thank you so much

Best
M J Hasan
PhD Student
Mechanical Engineering
University of Maine.

[Daniele Varsano]

Dear Hasan,

1) When using "slab z" the other coulomb parameter are ignored. RandQpts and RandGvec are also reasonable, and you do not need to converge.
2) When using the coulomb cutoff Re(eps(q=0)) ~1. If you obtain a different value, you are probably looking at a calculation without the coulomb cutoff. This is the eps_3d and its value will depend on the size of your supercell. You can also use eps_3d to recover the alpha using Eq.16. The eps obtained using the cutoff should be not considered instead.
3) Yes

Best,
Daniele