1) you are going to get band folding: by making the cell 2x larger the reciprocal space gets 2x smaller, and the bands are folded back in. You will get the same bands as before at the same absolute cartesian k-point but will also get bands folded back onto the same k-point by translation in the new small reciprocal unit cell. This is well described in classical solid-state textbooks (Ashcroft Mermin chap 9).
- band structure for free electrons pi/a = 0.5
The k values are absolue (bohr-1) so we can compare with the larger unit cell case.
- band structure for free electrons in a 2x larger unit cell.
a' = 2a so now the Brillouin Zone only extends to 0.25 bohr-1.
In relative coordinates, this is still 1/2 G, but G is shorter
- The bands (magenta and cyan) from neighboring supercell Brillouin Zones have to be folded back
2) Further, as your new reciprocal lattice vectors are smaller, you should not reduce the fractional coordinates of the vectors. To get the same path in k-space you need to augment the fractional k-point coordinates so that the absolute position is still the same.
Or, just pop over to Richard Martin's. If anyone can explain it to you, he can.
Matthieu
Hi there,
I'm trying to plot the e-band structure of 2*2*2 silicon cell and confirm that it is the same as the primitive cell. However, I am not getting the same thing. Can anyone help me to find what I'm doing wrong?
I made the lattice constant twice as big, left the rprim the same, and put 16 atoms in the cell.
For k points, I reduced the k point fractional coordinates by 1/2 as shown below.
Is this how you plot it? or am I doing something totally wrong?
Thanks for the help!!
kptbounds2 0.25 0.0 0.0 # L point
0.0 0.0 0.0 # Gamma point
0.0 0.25 0.25 # X point
0.5 0.5 0.5 # Gamma point in another cell.
tolwfr2 1.0d-20
enunit2 1 # Will output the eigenenergies in eV
#Definition of the unit cell
acell 3*20.434 # This is equivalent to 10.217 10.217 10.217
rprim 0.0 0.5 0.5 # FCC primitive vectors (to be scaled by acell)
0.5 0.0 0.5
0.5 0.5 0.0
#Definition of the atom types
ntypat 1 # There is only one type of atom
znucl 14 # The keyword "znucl" refers to the atomic number of the
# possible type(s) of atom. The pseudopotential(s)
# mentioned in the "files" file must correspond
# to the type(s) of atom. Here, the only type is Silicon.
#Definition of the atoms
natom 16 # There are two atoms
typat 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 # They both are of type 1, that is, Silicon.
xred # This keyword indicate that the location of the atoms
# will follow, one triplet of number for each atom
0 0 0
0 0.5 0
0 0 0.5
0.5 0 0
0.125 0.125 0.125
0.125 0.625 0.125
0.125 0.125 0.625
0.5 0.5 0
0.5 0 0.5
0 0.5 0.5
0.625 0.125 0.625
0.625 0.625 0.125
0.625 0.125 0.125
0.5 0.5 0.5
0.125 0.625 0.625
0.625 0.625 0.625
--
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Jedo Kim,
Heat Transfer Physics Laboratory
2350 Hayward, 2186 GG Brown Bldg.
University of Michigan, Ann Arbor, MI 48109-2143
Email: jedokim@umich.edu, jdzbox@hotmail.com
Tel: 734-764-3487 (o); 734-276-8370 (cell)
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