Dirac point in graphene

[jmullen]

Greetings all

I have been unsuccessful at generating a proper band structure for graphene using the GW options and I need help if someone in this forum has done it before. Let me begin by describing the process:

(1) Run a PW scf calculation (Quantum Espresso)
(2) Run a PW nscf calculation
(3) p2y -N at command line (not submitted to parallel process queue)
(4) yambo -i -V 2 (to see the number of plane waves being used in init run)
(5) yambo
(6) yambo -x -p p -g n -V 2 (generate the input file)
(7) yambo

Attached is a tarball of representative, but by no means complete, files of these calculations.

The problem is the persistent gap at the Dirac point. The gap has improved from my initial runs (0.8 eV down to 0.02 eV) but I am unable to close the gap completely.

QP [eV] @ K [469] (iku): 0.333333 0.500000 0.000000
B=1 Eo=-12.44 E=-18.35 E-Eo= -5.91 Z=0.86 So= 1.62981 xx=-24.17079 Vxc=-15.69168
B=2 Eo=-12.44 E=-18.28 E-Eo= -5.83 Z=0.86 So= 1.61910 xx=-23.90832 Vxc=-15.53331
B=3 Eo=-10.78 E=-14.96 E-Eo= -4.18 Z=0.87 So= 1.56363 xx=-21.25340 Vxc=-14.87560
B=4 Eo= 0.00 E= 1.14 E-Eo= 1.14 Z=0.89 So= 0.14934 xx=-11.73359 Vxc=-12.85598
B=5 Eo= 0.00 E= 1.16 E-Eo= 1.16 Z=0.89 So=-.1587 xx=-11.46 Vxc=-12.92


The variables I am changing (I think they are the most relevant to convergence) are the FFTGvecs, EXXRLvcs, GbndRange, and NGsBlkXp values. I have tested many different permutations of these variables and have watched the band structure (specifically the Dirac point) converge only to fail due to WF allocation failures (which I have mentioned before in previous posts). Lately, I have had access to an XT system with more memory and have seen better results, however still have failed to close the gap and I fear that my parameters for FFTGvecs and EXXRvcs are so small now that I am not converged and am fooling myself with a mistaken gap; it is only what I want by accident, not by convergence. Again, however, when increasing the number of vecs, bands, or NGsBlkXp, I cause the run to crash as before with an error message like below:

<---> [01] Job Setup
<---> [02] Input variables setup
<---> [02.01] Unit cells
<---> [02.02] Symmetries
<---> [02.03] RL shells
<---> [02.04] K-grid lattice
<09s> [02.05] Energies [ev] & Occupations
<10s> [03] Transferred momenta grid
<10s> [M 0.046 Gb] Alloc qindx_X qindx_S (0.019)
<13s> [04] External QP corrections (X)
<13s> [05] External QP corrections (G)
<13s> [06] EX(change)S(elf-energy) and Vxc potential
<13s> [M 2.054 Gb] Alloc WF (2.002)_pmii_daemon(SIGCHLD): PE 276 exit signal Killed

At step (1), I have converged graphene input files, at step (2), I have tried different k grid densities in order to have more QP's available in the GW calculation, I have run step (3) in parallel mode as well as single processor, but single processor is just easier since the configuration is small and does not require much time. At step (4), I have edited for smaller numbers of vectors as well as run defaults and the final steps have been run with so many different configuration tests that I cannot hope to address them here.

Any help is greatly appreciated, as I cannot move on to my actual topic of interest until I have successfully managed this planar system calculation.

[Daniele Varsano]

Dear Jeff,
I've no experience on this planar system, anyway you have a very small difference!!!
Try to look in this reference if they give some details of their calculations, even if I doubt!!
P. Trevisanutto et. al. PRL 101,226405 (2008).

In your tests of convergences you are not mentioning the k-point sampling,
do you have a 2D or 3D k-point mesh? In the case you have a 2D mesh may
the Random Integration Method is needed to integrate the coulomb potential
in the Bz for your self-energy.
I dont know if it helps,

Daniele

[jmullen]

Danielle,

Thanks for your response. First, the grid I am using (from the nscf file) is 72x72x1. While I am encouraged by the small gap, I would be thrilled by 0.005 eV

Seriously though, my concern is less with the value of the gap than the way in which I achieved it. When yambo -i is run, the default number of G vecs is nearly 140000, but in order to both close the gap and prevent memory allocation failure, I was only able to use 1000 - 1500 (FFTGvecs and EXXRLvcs). My concern is that this is seriously under converged and the gap is small by accident, not by accurate calculation. Is there any guidance you can give me on this concern?


Finally, I will revisit the paper you recommend, but as I recall, when I last read it there was little in the way of GW parameter information.

Thanks again

[Daniele Varsano]

Dear Jeff,

I was only able to use 1000 - 1500 (FFTGvecs and EXXRLvcs). My concern is that this is seriously under converged and the gap is small by accident, not by accurate calculation. Is there any guidance you can give me on this concern?

Well, such variables surely affect your <Vxc> and <Sigma_x> values, and then your gap.
If you have such a limit, my suggestion is just to look at the Sigma_x for instance, which is quite fast calculation:
yambo -x, then selecting just the Dirac point for the 2 bands you are interested in,
%QPkrange # [GW] QP generalized Kpoint/Band indices

and try to look the behaviour of <SIgma_x> varying EXXRLvcs until you can (100-500-1000-1200...). From that behaviour
you can have an idea from how far you are from convergence. The same, you can look at <V_xc> varying you FFTGvecs.

Good luck,

Daniele

[claudio]

Usually the convergence with the number of plane waves is quite fast, expecially if you didn't put a large distance between your
graphene planes. But rembemer that the GW correction converge slowly with the plane distance.

Also the number of k-points to converge the GW corrections is not so large, in particular in the paper of Trevisanutto et al.
they used just a 10x10x1 grid, and then they shifted it to obatin the band structure along different lines.

About the gap, check also the converge tresheld you used in PWSCF, a small difference in the wave-function,
can generate a small gap, moreover in the reference 29 of Trevisanutto, also they found a small gap of few meV but "..below the tipical numerical error
of ab-initio calculations and so compatible with 0 band gap" and I agree with them.