Kpt boundaries for cubic supercell

Question

I have a question on how to make a supercell in abinit.

I am trying to calculate the EBS of a cubic perovskite supercell (2x2x2 cubic STO). The geometry information can be found on the MP here. I need the supercell to simulate a doped system.

I have followed the abinit documentation regarding the supercell of Hydrogen here and the unfolding of the Brillouin zone here, although I find it not complete.

I start from the standard k-path for a cubic structure in the primitive cell.

kptopt2        -5   
kptbounds2
            0.0   0.0   0.0  #  Gamma
            0.0   0.5   0.0  #  X
            0.5   0.5   0.0  #  M
            0.0   0.0   0.0  #  Gamma
            0.5   0.5   0.5  #  R
            0.0   0.5   0.0  #  X

I have tried several paths, such as the following, trying to include all the “half” points and making sure to substitute G->X with -X/2->G->X/2 and I get a bunch of spikes.

kptopt2    -9 
kptbounds2
           -0.25 -0.25  0.0  # -M/2
            0.0  -0.25  0.0  # -X/2
            0.0   0.0   0.0  #  Gamma
            0.0   0.25  0.0  #  X/2
            0.25  0.25  0.0  #  M/2
            0.0  -0.25  0.0  # -X/2
           -0.25 -0.25 -0.25 # -R/2
            0.0   0.0   0.0  #  Gamma
            0.25  0.25  0.25 #  R/2
            0.0   0.25  0.0  #  X/2

Could it be that this is still incomplete and I am missing points such as 0.25 0.5 0.0 and 0.5 0.25 0.0 for M and 0.5 0.25 0.25 for R (etc…?).

Thank you

Marco

Answer 1

Ciao Marco!

Once you make the supercell the reciprocal lattice vectors are divided by 2 (or whatever factor) automatically. The kptbounds are in reduced coordinates so no need to change the bound. What will happen is the bands will fold back, so the new Gamma->X path will contain 8x as many bands (2x2x2) folded from the old Gamma->X as well as Gamma+(0,0,0.5)->X+(0,0,0.5) etc...

What you probably want is to unfold the bands to compare (once you add a defect) to the pristine bands and project on those. This can be done with several utilities with interfaces to abinit, in particular fold2bloch (https://docs.abinit.org/tutorial/fold2bloch/) and I think also https://github.com/mailhexu/banddownfolder (made for phonons and magnons, but I have seen a version work with electrons as well).