Dielectric constant of MoS2

Submitted by kanak on Sun, 03/12/2017 - 18:22

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Dear researchers

I have been trying to model the absorption spectrum of monolayer MoS2 with Berkeley GW. The LDA bandstructure is direct and gives a bandgap of about 1.8 eV. However while simulating epsilon, I am getting 0.92001322 for inverse epsilon (q->0, g=0, g'=0). Which means that the macroscopic dielectric constant should be 1.08. Which is not close to the value reported for MoS2 in literature.
Moreover, my GW bandstructure looks out of shape. I have simulated with a single shot GW method (G0W0). Some of the simulation parameters are given below:

Energy cutoff for epsilon: bare coulomb- 20 Ryd, screened coulomb= 60 Ryd
number of bands included: 96
K points used: for Wfn_co: 9 x 9 x 1
for Wfn: 18 x 18 x 1

I have redone the simulation with eqp update is sigma step. The quasiparticle bandstructure however, did not improve. For you convenience, I am attaching a file here:
https://drive.google.com/open?id=0B4eLXFpJHBhCbC1obGVMNVhZR2c

Can you please suggest what could I possibly do to get an improvement of the GW bandstructure and get the more accurate value of macroscopic dielectric constant?

Thanks
Kanak Datta
University of Michigan
Ann Arbor

Submitted by babarker on Mon, 03/13/2017 - 16:45

Hello Kanak,

Those parameters are not converged. Please refer to Diana Y. Qiu, Felipe H. da Jornada and Steven G. Louie, "Optical Spectrum of MoS2: Many-Body Effects and Diversity of Exciton States," Phys. Rev. Lett. 111, 216805 (2013), which is listed on the "Literature" page of this website.

Best,
Brad

Submitted by dyq on Mon, 03/13/2017 - 18:27

Hi Kanak,

Please take a look at this PRB for some parameters for monolayer MoS2:

https://journals.aps.org/prb/abstract/10.1103/PhysRevB.93.235435

A couple more points to add:

1. For a 2D material, epsilon(q->0) is no longer the bulk dielectric constant. Instead, it should be close to 1. q->0 is the long wavelength limit, and if you think about long wavelength in 2D, you can imagine that most of the electric field passes through the vacuum, so epsilon=1. This is discussed in more detail in the above paper.

2. I assume that you had a typo and 60 Ry is your BARE Coulomb cutoff, not screened. 60 Ry seems a little low for Mo, including d-states. Are you sure you're using norm-conserving pseudo-potentials?

3. The number of bands is related to the screened cutoff. If you use 96 bands, your effective screened cutoff is ~2Ry rather than 20 Ry. Please see the above paper for more details. You can also take a look at the convergence talk from the BerkeleyGW workshop.

Best,
Diana

Submitted by kanak on Tue, 03/14/2017 - 09:18

Hello

Thanks Diana for the reply. I have gone through the paper up to QP bandstructure calculation. I have some minor confusions:
1 When referring to Number of bands, do you refer to bands in epsilon and sigma calculation only or the total number of bands used in self-consistent and bands calculation in mean field step as well? Besides from the wfn file I see that only 9 valance bands are occupied for the MoS2 monolayer.
2. The k grids mentioned in literature, I am assuming they are coarse k grid sampling of the Brillouin zone in wfn_co.
3. I could not really get the part: 96 bands corresponds to effectively 2 Ryd in screened coulomb cutoff. Could you please be a little bit clear?
4. Before moving to QP bandstructure calculation, is there any way to be sure that the calculations are somewhat correct up to epsilon step? QP energy calculation using sigma is really a time-consuming step and it takes a lot of time for getting results.
Come corrections:
1. I made a typo regarding screened and bare coulomb cutoff energies in my post.
2. I am using norm-conserving pseudopotential.

Thanks again for the reply.

Kanak

Submitted by dyq on Tue, 03/14/2017 - 17:29

Hi Kanak,

1. The number of bands refers to the number of bands in epsilon and sigma.

2. The k-point sampling refers to the grid used to calculate epsilon. In BGW, this is WFN.

3. Each band has an energy. If the energy of the highest band is not roughly on par with the screened cutoff, then you're artificially truncating the screened cutoff to the energy of the highest band. I strongly recommend you take a look at the convergence tutorial and slides from the BerkeleyGW workshop: https://sites.google.com/site/berkeleygw2015/about . In general, it's always important to do convergence tests before starting large-scale calculations on a new material.

4. For the QP band structure, to save cost, I suggest you don't calculate the entire bandstructure before you're sure of your parameters. Just focus on a couple important k points, such as K and 0.5*K in MoS2.

Best,
Diana

Submitted by kanak on Fri, 03/24/2017 - 04:28

Hi

Can anyone please specify, how do I check the convergence of epsilon calculation after a run of epsilon.x?

Thanks
Kanak

Submitted by babarker on Fri, 03/24/2017 - 12:43

The file chi_converge.dat shows the convergence with respect to empty states of epsilon_(G=0,G'=0) (q, omega) and epsilon_(G=Gmax,G'=Gmax) (q, omega) for each q, for each omega.

To check how to systematically converge parameters for converged calculations of the quasiparticle band gap, see https://sites.google.com/site/berkeleygw2015/about, as Diana suggested, and/or read the supplementary information from the paper

Brad D. Malone and Marvin L. Cohen, "Quasiparticle semiconductor band structures including spin-orbit interactions," J. Phys.: Condens. Matter 25, 105503 (2013).

(The link is in the "Literature" page.)

Submitted by kanak on Tue, 04/04/2017 - 08:12

Hi

In the convergence talk and papers, it is suggested to start with a small number of K points i.e. 2x2x2. Can this same method of convergence be applied for 2D materials as well?

Thanks
Kanak