[Pw_forum] Reciprocity of Supercells & BZ Sampling

[yavar pour azar]

Dear QE users,

I have a conceptual problem with k-point sampling in supercells.

Suppose we have a simple cubic unit cell for the bulk, which it's
electronic structure, total energy and etc... is calculated by n*n*n BZ
Sampling.
for example I can see band width and band curvature along k axis, and i
will have max and min points for every band in different k_points such
gamma, X, L,......

Now, if we want to make a n*n*n supercell from this unit cell, it is the
known fact that just gamma point calculations is enough.

Anyone can see following sentences in most QE tutorials;
"Increase supercell in real space by a factor N along a ; EXACTLY same
results obtained by reducing  divisions in k mesh (in the new smaller BZ)
by factor N"

This is the problem that I cant understand : when we substitute the unit
cell by n*n*n  supercell ( k=0), the calculated bands with new sampling has
no curvature and extension along k axis, because we have just a K point.
Total Energy, probably is same as former unit cell (by integer factor), but
if we will lose information about other aspects of electronic structure by
this sampling?

I would appreciate it if anyone can help me to understand this, or refer me
to a source.


PS:  suppose supercell sustained no relaxation or similar changes, and we
have just the two different scales from one infinite, periodic lattice.



Thanks in advance.

Yavar Taghipour Azar
PhD student
Physics Group, AEOI, Tehran, Iran
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