How to decide the GW energy gap?

[Zafer Kandemir]

Dear Daniele,

My hexagonal structure has an indirect-band gap from the result of pwscf calculation. I attached the result of the band structure. CBMin is near the M point at the 88th data. In addition, I show the k-points data and weights in the units of cartesian coordinates:

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     number of k points=   169
                       cart. coord. in units 2pi/alat
        k(    1) = (   0.0000000   0.0000000   0.0000000), wk =   0.0011338
        k(    2) = (   0.0000000   0.0274929   0.0000000), wk =   0.0068027
        k(    3) = (   0.0000000   0.0549857   0.0000000), wk =   0.0068027
        k(    4) = (   0.0000000   0.0824786   0.0000000), wk =   0.0068027
        k(    5) = (   0.0000000   0.1099715   0.0000000), wk =   0.0068027
        k(    6) = (   0.0000000   0.1374643   0.0000000), wk =   0.0068027
        k(    7) = (   0.0000000   0.1649572   0.0000000), wk =   0.0068027
        k(    8) = (   0.0000000   0.1924501   0.0000000), wk =   0.0068027
        k(    9) = (   0.0000000   0.2199430   0.0000000), wk =   0.0068027
        k(   10) = (   0.0000000   0.2474358   0.0000000), wk =   0.0068027
        k(   11) = (   0.0000000   0.2749287   0.0000000), wk =   0.0068027
        k(   12) = (   0.0000000   0.3024216   0.0000000), wk =   0.0068027
        k(   13) = (   0.0000000   0.3299144   0.0000000), wk =   0.0068027
        k(   14) = (   0.0000000   0.3574073   0.0000000), wk =   0.0068027
        k(   15) = (   0.0000000   0.3849002   0.0000000), wk =   0.0068027
        k(   16) = (   0.0000000   0.4123930   0.0000000), wk =   0.0068027
        k(   17) = (   0.0000000   0.4398859   0.0000000), wk =   0.0068027
        k(   18) = (   0.0000000   0.4673788   0.0000000), wk =   0.0068027
        k(   19) = (   0.0000000   0.4948717   0.0000000), wk =   0.0068027
        k(   20) = (   0.0000000   0.5223645   0.0000000), wk =   0.0068027
        k(   21) = (   0.0000000   0.5498574   0.0000000), wk =   0.0068027
        k(   22) = (   0.0000000  -0.5773503   0.0000000), wk =   0.0034014
....

In the output of the o.qp file:

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# QP @ K 1 - 169 : b 20 - 21
#
#    K-point      Band         Eo           E-Eo         Sc|Eo
#
     1.00000     20.00000      0.00000      0.05754      1.99238
     1.00000     21.00000      1.67690      1.61105     -4.50922
    2.000        20.00       -.7489E-3    0.6371E-1     2.000   
     2.00000     21.00000      1.66505      1.60199     -4.51936
    3.000        20.00       -.2382E-2    0.8191E-1     2.016   
     3.00000     21.00000      1.62924      1.57633     -4.54363
    4.000        20.00       -.4455E-2    0.1101        2.030   
     4.00000     21.00000      1.56905      1.53770     -4.56607
    5.000        20.00       -.8334E-2    0.1441        2.038   
     5.00000     21.00000      1.48451      1.49372     -4.56885
    6.000        20.00       -.1656E-1    0.1792        2.038   
     6.00000     21.00000      1.37744      1.44851     -4.54073
     7.00000     20.00000     -0.03118      0.21232      2.03424
     7.00000     21.00000      1.25215      1.40614     -4.48052
     8.00000     20.00000     -0.05279      0.24154      2.02731
     8.00000     21.00000      1.11514      1.36526     -4.39391
     9.00000     20.00000     -0.08041      0.26587      2.01987
     9.00000     21.00000      0.97391      1.32537     -4.28905
    10.00000     20.00000     -0.11189      0.28505      2.01459
    10.00000     21.00000      0.83587      1.28873     -4.17349
    11.00000     20.00000     -0.14437      0.29872      2.01620
    11.00000     21.00000      0.70769      1.25502     -4.05453
    12.00000     20.00000     -0.17482      0.30648      2.03308
    12.00000     21.00000      0.59483      1.22527     -3.94076
    13.00000     20.00000     -0.20067      0.30791      2.07642
    13.00000     21.00000      0.50148      1.20037     -3.84211
    14.00000     20.00000     -0.22043      0.30302      2.15526
    14.00000     21.00000      0.43056      1.18103     -3.76655
    15.00000     20.00000     -0.23423      0.29306      2.26779
    15.00000     21.00000      0.38361      1.16672     -3.71374
    16.00000     20.00000     -0.24366      0.28056      2.39669
    16.00000     21.00000      0.36054      1.15548     -3.67140
    17.00000     20.00000     -0.25078      0.26856      2.51679
    17.00000     21.00000      0.35892      1.14582     -3.62267
    18.00000     20.00000     -0.25702      0.25910      2.61052
    18.00000     21.00000      0.37358      1.13592     -3.55980
    19.00000     20.00000     -0.26270      0.25261      2.67459
    19.00000     21.00000      0.39714      1.12668     -3.48938
    20.00000     20.00000     -0.26742      0.24872      2.71423
    20.00000     21.00000      0.42148      1.11864     -3.42532
    21.00000     20.00000     -0.27056      0.24690      2.73537
    21.00000     21.00000      0.43940      1.11320     -3.38077
    22.00000     20.00000     -0.27166      0.24652      2.74186
    22.00000     21.00000      0.44595      1.11147     -3.36443
    .....

Actually, I know these points:
Gamma point denotes (k-point:1.0, Valence Band maximum:20.0)
M point denotes (k-point:22.0, Conductance Band Minimum:21.0)

In the calculation of the GW energy gap, I use the following result for the Gamma point. I am sure.

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     1.00000     20.00000      0.00000      0.05754      1.99238 

How can I sure which band is the CBM?

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     ??.00000     21.00000      -             -              - 

Best regards.

[Daniele Varsano]

Dear Zafer,
I'm not sure I've understood your question.
In the o.qp file you have both the KS structure as calculated by QE and the GW correction so you should be able to identify the CBM.
In addition, you can calculate the GW bandstructure along a given path by using the ypp utility by using the variable:
GfnQPdb= "E < ./path/ndb.QP"
See here Step.3 for a tutorial:
http://www.yambo-code.org/wiki/index.ph ... rial:_h-BN

Best,
Daniele

[Zafer Kandemir]

Dear Daniele,

Thank you for replying. I know the GW band structure calculation with ypp utility. My question is actually which k-point denotes the CBM in the Yambo calculation?
If an indirect energy gap was at the Gamma and M points, Egap=E_CBM( 0.44595 + 1.11147)[22. k-point] - E_VBM( 0.0 + 0.05754)[1. k-point] = 1.49988 eV in the Yambo calculation.

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#    K-point      Band         Eo           E-Eo         Sc|Eo
#
     1.00000     20.00000      0.00000      0.05754      1.99238   FOR GAMMA POINT
    22.00000     21.00000      0.44595      1.11147     -3.36443   FOR M POINT

However, in my pwscf result, the value of the conductance band minimum is between Gamma and M points. I can't decide the k-point number (1:22) in Yambo calculation.

Best regards.

[Daniele Varsano]

Dear zafer,
Still I do not get your problem.
The cbm at gw level can be found in a different point of the bz with respect the dft position due to different gw corrections. Just be sure that this is the case.

Best,
Daniele