[Solved] Supercell bands

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[Solved] Supercell bands

Postby LThulin » Thu Feb 25, 2010 8:55 pm

I have a question concerning supercell bands vs bulk bands. I have a tetragonal cell (a,0,0),(0,a,0) (0,0,c) and the bulk band calculation yields the expected result for all k paths. I make a supercell that is double the volume of the conventional cell by rotating the cell using the new vectors (a*sqrt(2),a*sqrt(2),0) (a*sqrt(2),-a*sqrt(2),0) (0,0,c). So the vector along lattice constant 'c' is unchanged. So the question is whether I should expect to recover the band plot for the supercell geometry exactly or if BZ folding issues come into play here too, even along a k path such as Z:Gamma (0,0,1/2):(0,0,0), i.e. perpendicular to the (001) plane where the lattice vector is unchanged. I've included a band plot of the supercell for this path and the blue squares are the highest valance band and lowest conduction band for bulk. There is a lot of agreement near gamma, but not Z. However, it seems to me that the bulk bands can be recovered by contributions from several different supercell bands. And what of the supercell energies above the highest valance bulk band near Z? Are they a result of BZ folding or do they indicate that I'm doing something wrong?

Thanks,
Luke Thulin
Attachments
Graph3.jpg
Z:Gamma path
Last edited by LThulin on Fri Feb 26, 2010 6:05 pm, edited 1 time in total.
LThulin
 
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Re: Supercell bands

Postby gonze » Thu Feb 25, 2010 9:48 pm

Dear Luke,

With your new supercell, you have twice more bands in each of the points of the Brillouin zone,
including the Gamma-Z line. Indeed, while all the bands that were present in the original cell
along the Gamma-Z line (0 0 0)-(0 0 1/2) are indeed unchanged in the new Gamma-Z line (0 0 0)-(0 0 1/2),
that corresponds moreover to the
same length in reciprocal space (because the c value did not change), there is another
line in the original cell, that is parallel to the Gamma-Z line, with coordinates (1/2 1/2 0)-(1/2 1/2 1/2)
that will be folded into the new Gamma-Z line.

Best,
X
gonze
 
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