Diagonal Coulomb components

[clin]

Dear developers,

I have a question on the diagonal approximation of Coulomb potential. According to this Yambo tutorial (https://www.yambo-code.eu/wiki/index.ph ... al_systems), when RIM method is used for Coulomb potential, I noticed that only the diagonal components of Coulomb potential are calculated. If I understand correctly, when calculating screened W in GW or BSE application in this case, the wing term of dielectric matrix is dropped. Is this correct?

Code: Select all

Gamma point sphere radius         [au]:  0.08028
 Points outside the sphere             :  799246
 [Int_sBZ(q=0) 1/q^2]*(Vol_sBZ)^(-1/3) = 7.665674
                                should be < 7.795600
 [WR./2D_WR//ndb.RIM]--------------------------------------
  Brillouin Zone Q/K grids (IBZ/BZ):   7   36    7   36
  Coulombian RL components        : 111
  Coulombian diagonal components  :yes
  RIM random points               : 1000000
  RIM  RL volume             [a.u.]: 0.390293
  Real RL volume             [a.u.]: 0.390112
  Eps^-1 reference component       :0
  Eps^-1 components                : 0.00      0.00      0.00
  RIM anysotropy factor            : 0.000000
 - S/N 005962 -------------------------- v.04.01.02 r.00120 -

Then the full Coulomb matrix of RIM is done by adding QpgFull into input. What happens if RIM is not used? Will the Coulomb potential also be diagonal in the case of bulk materials (i.e. no RIM)?

[Daniele Varsano]

Dear Changpeng,

the off-diagonal coulomb components are always taken into account. The diagonal/non-diagonal keyword (QpgFull) refers to the RIM, i.e. if the RIM is also applied to off-diagonal (wings) elements.

Best,
Daniele

[clin]

Dear Daniele,

Thanks for your help. I have one further question: is it possible to dope the system in Yambo? For example, I want to calculate the dielectric matrix and screened Coulomb potential of doped graphene. Is there a way in Yambo that I can rigidly shift the Fermi level of the system? By checking the Yambo inputs, it seems I can manually set the variable "Nelectro" to change the Fermi level. If so, when I change it, will it cause any potential problem?

Best,
Changpeng

[Daniele Varsano]

Dear Changpeng,

yes, as you argued, you need to the N electron variable. This will apply a rigid shift of the Fermi energy on the electronic structure calculated on the undoped system.
Another way is to dope the system in QE and proceed in a standard way. If a rigid shift approximation can be applied the two ways should provide very similar results.

Best,

Daniele