Erroneous band structure of GaAs

[Dae kwang Jun]

Dear everyone,

I am trying to compute the bandstructure of GaAs with Elk. However, the results do not match with literature. Here is the file that I am using to obtain it.

tasks
0
20

xctype
20

autolinengy
.true.

mixtype
1

maxscl
200

nempty
15

sppath
'/home/jdk/Downloads/elk-4.0.15/species/'

primcell
.true.

avec
-5.196700000 -5.196700000 0.000000000
-5.196700000 5.196700000 0.000000000
-5.196700000 0.000000000 -5.196700000

atoms
2 : nspecies
'Ga.in' : spfname
1 : natoms; atposl, bfcmt below
0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
'As.in' : spfname
1 : natoms; atposl, bfcmt below
0.75000000 0.25000000 0.50000000 0.00000000 0.00000000 0.00000000

ngridk
6 6 6

vkloff
0 0 0

plot1d
3 100
0.5000 0.5000 0.5000
0.0000 0.0000 0.0000
0.5000 0.0000 0.5000

Here is the bandstructure that I am comparing it with: http://th.fhi-berlin.mpg.de/th/fhi98md/doc/main/node19.html

The k vectors in the file are from the Bilbao Crystallographic server.

[martin_frbg]

Did you compare the structural part of your input to what is in examples/basic/GaAs ?

[J. K. Dewhurst]

I think Martin is correct: you are using a non-conventional set of lattice vectors. Try using those in the example and redo the plot.

Cheers, Kay.

[Dae kwang Jun]

Dear John Kay Dewhurst,

I get the correct bandstructure if I use avec and atoms from the example/basic/GaAs/elk.in. However, I would greatly appreciate further feedback. The input for avec and atoms was generated using the spacegroup utility in Elk.
Here is the input that I used for the spacegroup utility:

'F-43m'
10.3934 10.3934 10.3934
90.0000 90.0000 90.0000
3 3 3
.true.
2
'Ga'
1
0.00000000 0.00000000 0.0000000
'As'
1
0.25000000 0.25000000 0.2500000

The Wyckoff positions and lattice constants are from the ICSD. The lattice constants have been converted to Bohr radii. In the ICSD they are in angstrom.
I also tried

'F-43m'
10.3934 10.3934 10.3934
90.0000 90.0000 90.0000
1 1 1
.false.
2
'Ga'
1
0.00000000 0.00000000 0.0000000
'As'
1
0.25000000 0.25000000 0.2500000

However, the output for this produces 8 atomic positions (the example has 2, which should be the case for PBC).

I also tried

'F-43m'
10.3934 10.3934 10.3934
90.0000 90.0000 90.0000
1 1 1
.true.
2
'Ga'
1
0.00000000 0.00000000 0.0000000
'As'
1
0.25000000 0.25000000 0.2500000

This gives me a different GEOMETRY.OUT file than for the 3 3 3 .true. case. But the bandstructure is still wrong.

What is wrong with this input? The spacegroup utility seems to work well in other cases so it is puzzling that it gave me the wrong output for this calculation.

[Lars Nordström]

There is nothing wrong with either elk or spacegroup. Your calculations are probably OK.

However when you want to plot the band-structure you have to give the symmetry points in terms of the current reciprocal lattice vectors. The different settings correspond to different choices of reciprocal lattice vectors, so you have to see what the two non-trivial symmetry points, in the plot1d block below, become with your "choice" of reciprocal lattice vectors.

With the "standard" setting the reciprocal lattice vectors are something like
0.5 0.5 -0.5
0.5 -0.5 0.5
-0.5 0.5 0.5
So your given symmetry points are in Cartesian coordinates
0.5 0.5 0.5
0 0 0
0 0.5 0.0
You now have to transform these Cartesian coordinates to partial reciprocal lattice vectors
with the choiec of reciprocal lattice vectors as given in the beginning of INFO.OUT.

In short: there are many correct choices of setting up the structure, but the actual form of the symmetry k-points dependent on this choice. Clearer?

Good luck!
Lars

---

plot1d
3 100
0.5000 0.5000 0.5000
0.0000 0.0000 0.0000
0.5000 0.0000 0.5000