Electron self energy in graphene

[sridhu88]

Hello,
I computed electron self-energy in graphene and was comparing my results with those in the literature. In particular, I am looking to reproduce, Fig. 1b of this paper: https://arxiv.org/pdf/0707.1666.pdf

My result for the self-energy for n-doped graphene (Fermi energy ~ 0.6 eV above Dirac point) at 20 K can be seen in this link: https://www.dropbox.com/s/3aw8szaizzyyn ... 0.png?dl=0

While the self-energy away from the Fermi energy appears to be in reasonable agreement with the paper, I'm unable to match the very low self-energy near the Fermi level and Dirac point. Similar to the paper, I have tried a very fine grid of 1000x1000 and I use a broadening of 10 meV. The only difference I can think of in my calculation is that the coarse scf calculations was only performed with a k-grid of 72x72x1 while in the paper they report a coarse grid of 96x96x1. Phonon dynamical matrix was computed using a 12x12x1 q-grid. The localization of Wannier functions is very good (<1 Angstrom) and the interpolated electron and phonon bandstructures match DFT bandstructures very well. I'm providing my epw input file below. Can anyone help me identify what could possibly be the problem with my calculation?

Many thanks!
Sridhar
-------------------------
EPW input file
--
&inputepw
prefix = 'graphene'
amass(1) = 12.01078
amass(2) = 12.01078

outdir = '/sandbox/sadasivam/graphene_temp/epw_12_12/'
iverbosity = 0

elph = .true.
epbwrite = .true.
epbread = .false.

epwwrite = .false.
epwread = .false.

! kmaps = .true.

nbndsub = 5
nbndskip = 0

wannierize = .true.
num_iter = 300
iprint = 2
dis_win_max = 15
dis_froz_min = -25
dis_froz_max = -2.5
proj(1) = 'C1:sp2;pz'
proj(2) = 'C2:pz'
wdata(1) = 'Begin Kpoint_Path'
wdata(2) = 'G 0.00 0.00 0.00 M 0.50 0.50 0.00'
wdata(3) = 'M 0.50 0.50 0.00 K 0.666667 0.3333334 0.00'
wdata(4) = 'K 0.6666667 0.33333334 0 G 0.00 0.00 0.00'
wdata(5)= 'End Kpoint_Path'
wdata(6) = 'bands_num_points = 50'
wdata(7) = 'bands_plot = .true.'
wdata(8) = 'kmesh_tol=0.0000000001'

efermi_read = .true.
fermi_energy = -1.6

band_plot = .true.

elecselfen = .true.
phonselfen = .false.
a2f = .false.

parallel_k = .true.
parallel_q = .false.

fsthick = 1.5 ! eV
eptemp = 20 ! K (same as PRB 76, 165108)
degaussw = 0.010 ! eV

dvscf_dir = '../ph_12_12/dvscf_dir/'
filukk = './graphene.ukk'
filkf = 'kpath.txt'
! filqf = 'qpath.txt'
nqf1 = 1000
nqf2 = 1000
nqf3 = 1

nk1 = 24
nk2 = 24
nk3 = 1

nq1 = 12
nq2 = 12
nq3 = 1
/
19 cartesian
0.0000000 0.0000000 0.0000000 0.0138889
0.0277778 -0.0481125 0.0000000 0.0833333
0.0555556 -0.0962250 0.0000000 0.0833333
0.0833333 -0.1443376 0.0000000 0.0833333
0.1111111 -0.1924501 0.0000000 0.0833333
0.1388889 -0.2405626 0.0000000 0.0833333
-0.1666667 0.2886751 0.0000000 0.0416667
0.0833333 -0.0481125 0.0000000 0.0833333
0.1111111 -0.0962250 0.0000000 0.1666667
0.1388889 -0.1443376 0.0000000 0.1666667
0.1666667 -0.1924501 0.0000000 0.1666667
-0.1388889 0.3367877 0.0000000 0.1666667
0.1666667 -0.0962250 0.0000000 0.0833333
0.1944444 -0.1443376 0.0000000 0.1666667
-0.1111111 0.3849002 0.0000000 0.1666667
-0.0833333 0.3367877 0.0000000 0.0833333
-0.0833333 0.4330127 0.0000000 0.0833333
-0.0555556 0.3849002 0.0000000 0.1666667
-0.0000000 0.3849002 0.0000000 0.0277778

[carla.verdi]

Dear Sridhar,

It seems to me that in the paper they report a coarse k grid of 72x72 so yours should be fine.
What about your results for pristine graphene?
In the paper they report using a 1000x1000 fine grid in the irreducible wedge though - could you try for example using 10^6 random points?

Best,
Carla

[sridhu88]

Hi Carla,
Sorry, I made a mistake in my original post. As you said, they used a coarse k-grid of 72x72x1 while I use a 24x24x1 coarse k-grid. But I felt this shouldn't matter that much (maybe I'm wrong?). Any thoughts on why even the coarse grid needs to be so fine?

The result for pristine graphene is also similar -- my self-energy near Fermi level is higher than what it should be. See plot here: https://www.dropbox.com/s/jbu9cfnpdj9ut ... e.png?dl=0

I haven't tried random q-points -- I can try that.

Thanks,
Sridhar

[carla.verdi]

Dear Sridhar,

I haven't seen convergence data regarding the coarse k grid sampling, however I would say that the use of such a large grid (72x72) cannot be casual, otherwise a much smaller, and more common, coarse sampling would have been used. It's probably linked to the difficulty in sampling properly the electronic properties, e.g. near the X point.
If you can't afford a 72x72 grid, I suggest you try with a larger grid than the 24x24 one you used, and see if your results change and get closer to the published ones.

Best,
Carla

[sridhu88]

Hi Carla,
Thanks for your response. I have tried a coarse k-grid of 72x72 for the phonon calculation and my results still don't match the published results (I still get a much higher self-energy near Fermi level). I have also tried plotting e-ph matrix elements to compare with Figure 2 of this paper: https://journals.aps.org/prb/abstract/1 ... .93.125432

Link to plot: https://www.dropbox.com/s/cuozgzckqqwgg ... 1.png?dl=0

These e-ph matrix elements are averaged over the two-linear electronic bands at K-point for phonon wavevectors from gamma to K. The matrix elements for the optical phonons are in reasonable agreement with the paper. However, the acoustic phonon matrix elements near Gamma are quite large and contradict the trend |g|~q expected from deformation potential theory. Any idea what could be going wrong here? I'm getting a sense that the electron-phonon matrix element interpolation near Gamma is going bad for some reason.

My coarse q-grid is 12x12. One thing I noticed is that the acoustic sum rule is not exactly satisfied. The gamma point frequencies of acoustic modes were {0.08, 0.18, 0.21} meV from EPW. The acoustic sum rule violation in the frequencies calculated directly from ph.x is even larger -- frequencies were of the order of 70-80 cminv.

Any help would be appreciated!
Best,
Sridhar

[sridhu88]

I resolved this problem and I thought I'll update here. I needed to use a dense coarse q-grid of 24x24x1 to obtain the correct self-energies near Fermi level. A 12x12x1 grid was not enough to obtain the correct e-ph matrix elements for acoustic phonons near Gamma point (see plot in my earlier post).

While the problem did get resolved, I'm curious to understand why such a fine phonon q-grid is needed for graphene? Please let me know if anyone has thoughts to share on this.
Best,
Sridhar

[carla.verdi]

Dear Sridhar,

Thank you for updating on your results! It might be related to the Kohn anomaly in graphene.

Best
Carla