2D system phonon dispersion curve

Hi Prof Julian,
Is it possible in GULP that I can simulate a 2D system and get the phonon dispersion curve for it?

I was trying to simulate a “square” lattice based with FPU-beta potential. The potential is identical to what “polynomial” potential looks like in GULP (I take c0=1,c1=0,c2=A,c3=0,c4=B).

A 2D system shall have only 2 acoustic branches for 1 basis atom. But I get 3 branches with GULP (which is probably because GULP simulates 3D system).

Is there a way to directly simulate 2D system in GULP?
And if not then do I need to remove the ZA branch by looking into its eigenvector manually (would that give the same picture if I simulate only 2D system?)

PS: I am attaching the GULP script file for the same.

disp.gin (448 Bytes)

Thank you in advace.

GULP can compute phonon dispersion in 2D. To do this you need to specify the structure as being 2D in the input though, rather than 3D (as in disp.gin). You need to use “svector” to specify the 2D (surface vectors) unit cell, rather than “vectors” which is for 3D.

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Thank you Prof Julian for your valuable suggestion but I have few more doubts.

I tried using the “svectors” but I have one confusion because of the kind of O/P I am getting from 2D system (file attached with name: disp2d.gin) .

(a) The O/P Ar.disp after running the GULP with 100 kpoints as I/P always gives total 99 kpoints in the [0.5,0,0] direction which should have been 100 kpoints.

(b) The starting line of “Ar.disp” says "# Section number = 1 Configuration = 1

Final K point = 0.000000 -0.000000 0.000000"

And this is not what my I/P was.

(c) As the system is 2D now, so the degrees of freedom becomes 2 and thus the no. of branches shoul now be 2. But the O/P gives 3 frequencies for a particluar kpoint. Is this correct?

(d) In a 3D system, if I simply remove the flexural curve will it give me the similar 2D dispersion curve which I should be getting from the 2D system? (I don’t think so as the DOF is restricted and so will be the DOS will get affected and also the phonon would be scattering differently)

For 2D:
dos2d.pdf (14.0 KB)
disp2d.pdf (7.4 KB)
2D I/P file: disp2d.gin (437 Bytes)

For 3D:
dos3d.pdf (14.1 KB)
disp3d.pdf (7.7 KB)
3D I/P file: disp.gin (448 Bytes)

Sorry for the long question, but your help will be greatly appreciated.

With regards,
Abhikeern

Hi Abhikeern,
I think a lot of your issues come from a problem in your input for the 2D case. If you have a 2D system then there are only 2 BZ directions and so the dispersion specification should be:

0.0 0.0 to 0.5 0.0

With this everything works for me and you get a 100 points in the disp file.
NB: There are always 3 frequencies per atom regardless of the dimensionality from 0 to 3-D since it has nothing to do with periodicity, but comes from the fact you are working in a 3-D Cartesian space.
Whether 3D is the same as 2D or not depends on if there is any interaction in the extra periodic direction. If there is no interaction then the results should be the same.
Regards,
Julian

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Thank Prof Julian. It is working now and thank you for the explanation as well.
With regards,
Abhikeern