[QE-users] Effective Mass Tensor unit-cell dependency

Wed Sep 22 11:42:08 CEST 2021

Dear Pietro,

I actually haven’t started thinking about which High Symmetry Points are comparable/identical going from one unit cell definition to the next. I was assuming that the Gamma Point (0,0,0) should be identical/equivalent no matter the representation of the unit cell.
I think your point is that the label/High Symmetry Point of the minimum might change when changing the Unit Cell. That is probably true, but still: I think the results for the Gamma Point should be identical, which it isn’t in my calculation.

All the best,

Carl-Friedrich Schön

Von: Pietro Davide Delugas<mailto:pdelugas at sissa.it>
Gesendet: Dienstag, 21. September 2021 13:25
An: Quantum ESPRESSO users Forum<mailto:users at lists.quantum-espresso.org>
Betreff: Re: [QE-users] Effective Mass Tensor unit-cell dependency

Sorry probably  I am misunderstanding you question.
Are you taking into account the  band folding when you compute the mass tensor in the cubic supercell ?
If I have understood well what you are doing, you should compare the conduction-band’s  effective masses at Gamma in the cubic  supercell with those at X in the fcc cell at X.

[Silicon - The Yambo Project]

Regards – Pietro

Sent from Mail<https://go.microsoft.com/fwlink/?LinkId=550986> for Windows

From: Schön, Carl-Friedrich<mailto:schoen at physik.rwth-aachen.de>
Sent: Tuesday, September 21, 2021 11:47 AM
To: Quantum ESPRESSO users Forum<mailto:users at lists.quantum-espresso.org>
Subject: Re: [QE-users] Effective Mass Tensor unit-cell dependency

Dear Paolo,

I take no responsibility to which unit cell is called what, I can never remember... Maybe my mind is too primitive to recognize the correct convention ;-)

I tried using ibrav=2 etc. for the 2-atom UC, but the results were (almost) identical to the ibrav=0 2-atom UC input:

(Tensor for ibrav=2)
0.882  , 0.0    , 0.0
0.0    , 0.294  , -1.47
0.0    , -1.47  , 2.352

(Slight difference as I used a slightly different lattice parameter, but the shape of the tensor is identical)

Hence not the one I would expect and see in the 8-atom UC. The reason I am using ibrav=0 is simply due to the way I generate my input files. As far as I understood it, it should not make a difference for the calculation, right?

Thanks and all the best,

Carl-Friedrich

Am 21.09.2021 um 15:49 schrieb Paolo Giannozzi <p.giannozzi at gmail.com<mailto:p.giannozzi at gmail.com>>:

Funny: I have always called "primitive" the 2-atom cell. "conventional" the 8-atom one. Anyway, the 2-atom diamond structure (fcc lattice) is simply
  ibrav=2, a=lattice parameter (A)
or
  ibrav=2, celldm(1)=lattice parameter (a.u.)
(lattice parameter=side of the cube) plus
ATOMIC_POSITIONS (alat)
Si 0.00 0.00 0.00
Si 0.25 0.25 0.25
or
ATOMIC_POSITIONS (crystal)
Si 0.00 0.00 0.00
Si 0.25 0.25 0.25
or any of the various possible ways of specifying atomic positions. If you do things properly you will find that the 2-atom and 8-atom cells give exactly the same results.

Paolo

On Mon, Sep 20, 2021 at 1:28 PM Schön, Carl-Friedrich <schoen at physik.rwth-aachen.de<mailto:schoen at physik.rwth-aachen.de>> wrote:
Dear QE users,

I have a question regarding the effective mass tensor, that I cannot seem to find the solution for. One could also rephrase this as a general question regarding the energy eigenvalues of k-points within different representations of unit-cells.
I have used QE to calculate the bands/eigenvalues of Silicon. I have done this ones with the conventional unit cell (from materials project):

Si2
1.0
3.8681383004362986 0.0 0.0
1.9340686210409386 3.349905532609194 0.0
1.9340686210409386 1.1166353539288019 3.1583211568194507
Si
2
Direct
0.250000000 0.250000000 0.250000000
0.000000000 0.000000000 0.000000000

As well as the primitive unitcell:
Si8
1.0
5.4687280655 0.0000000000 0.0000000000
0.0000000000 5.4687280655 0.0000000000
0.0000000000 0.0000000000 5.4687280655
Si
8
Direct
0.250000000 0.750000044 0.250000000
-0.000000000 -0.000000000 0.500000000
0.250000000 0.250000000 0.750000044
-0.000000000 0.500000000 0.000000000
0.750000044 0.750000044 0.750000044
0.500000000 0.000000000 0.000000000
0.750000044 0.250000000 0.250000000
0.500000000 0.500000000 0.500000000

Let's look at the gamma point only at this point: I then constructed (using the emc.py script) a cartesian k-point grid around the Gamma point in order to get the effective mass tensor for the gamma point for each definition of the unit cell (Conduction Band). For the primitive, 8 atom unit cell, I get something like:

-20.46496343 0.00000000 0.00000000
0.00000000 -20.46496343 0.00000000
0.00000000 0.00000000 -20.46496343

with all Eigenvalues being -20.465 (the tensors are given in units of 1/m*). As far as I am aware, this is what it should look like in terms of symmetry/degeneracy (the absolute values are not of interest at this point).

If I look at the conventional, 2 atom unit cell, I get something like:
0.88345374 -0.00018375 -0.00018375
-0.00018375 0.11245293 -1.46684926
-0.00018375 -1.46684926 2.17115005
with non-degenerate eigenvalues of -0.65, 0.88, 2.93.
I do not understand how this can be. I would understand that the tensors might look different due to different (absolute) orientation in k-space, but the eigenvalues should remain identical, should they not? Otherwise the physics would have changed. Especially in the example of the Gamma point above, I would have assumed to get the exact same tensor, as the effective masses are equal in all directions. Again, the dense grid around the Gamma point is constructed as cartesian cube in both cases.

I therefore looked at the eigenvalues (energies in the conduction band) of the nscf calculation of said dense grid:
Points that should be equivalent (and are indeed identical in the primitive 8 atom case) are not in the 2 atom case, e.g. E(0.01,0,0)!=E(0,0.01,0). I varied the spacing of the grid, but to no effect. The differences are also too big to be numeric errors:

Position:
5.8000000E-03   0.0000000E+00   0.0000000E+00
Eigenenergies:
   1       -5.811100
   2        5.989300
   3        5.997400
   4        6.001900
   5        8.550800 --> Conductino Band
   6        8.552000
   7        8.556000
   8        9.102700
   9       13.711000
  10       13.716400
  11       13.883000
  12       17.181200

Position:
  0.0000000E+00  -5.8500000E-03  -0.0000000E+00
Eigenenergies
   1       -5.811100
   2        5.988800
   3        5.998800
   4        6.000700
   5        8.549800 -->Conduction Band
   6        8.554400
   7        8.554800
   8        9.102800
   9       13.710800
  10       13.716400
  11       13.883100
  12       17.179600

Here the input I used for the scf calculation:

&control
calculation = 'scf'
prefix='Si_mp-149_computed_Relax_6'
tstress = .true.
tprnfor = .true.
pseudo_dir='/rwthfs/rz/cluster/home/NC'
outdir='tmp'
disk_io='low'
wf_collect=.true.
verbosity= 'high'
/
&system
ibrav =0,
nat=2
ntyp=1
ecutwfc = 100
ecutrho = 400
occupations = 'fixed'
/
&electrons
mixing_beta = 0.2
conv_thr = 1.0d-10
/
ATOMIC_SPECIES
Si 28.086 Si.upf
ATOMIC_POSITIONS {crystal}
Si  0.25  0.25  0.25
Si  0.0  0.0  0.0
CELL_PARAMETERS
7.309722  0.0  0.0
3.65486  6.330404  0.0
3.65486  2.110135  5.968362
K_POINTS {automatic}
24 24 24 0 0 0

I am not sure what I am missing… In my understanding the results should be (generelly) independent of the definitino of the used unit-cell…

Thank you and all the best,

Carl-Friedrich Schön, PhD Student, RWTH Aachen University
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--
Paolo Giannozzi, Dip. Scienze Matematiche Informatiche e Fisiche,
Univ. Udine, via delle Scienze 206, 33100 Udine, Italy
Phone +39-0432-558216, fax +39-0432-558222
_______________________________________________
Quantum ESPRESSO is supported by MaX (www.max-centre.eu<http://www.max-centre.eu>)
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