[Wannier] Supercells and symmetry

[Elias Assmann]

Dear Wannier list,

I am working on a t2g system with cubic symmetry, such that the t2g
bands are degenerate.  In particular, I am looking at the "simple"
(1x1x1) unit cell and a 1x1x2 supercell (no impurity or anything --
this is just for testing purposes).  Note also that I am using
Wien2k/Wien2Wannier.

My concern is that the symmetry between xy and xz/yz is broken in the
Wannier projection for the supercell.  (At the DFT level the symmetry
seems correct, meaning that the DOS and bandstructure agree, the
latter modulo backfolding of course).

I will follow up with details if desired, but maybe that is not even
necessary.  My basic question is: What level of symmetry can be
expected from Wannier90 in such a situation?  Is there anything
special one has to keep in mind?  In other words: What could I be
doing wrong?

I would be grateful for any pointers.

	Elias

PS: Maybe this seems like a trifling matter, but it is important to me
because eventually I want to study more non-trivial supercells and
look at the effect on the Wannier functions.  Therefore I need to be
able to compare the Wanniers from 1x1x1 and the supercell.

For instance, if I replace one of the target atoms in the 1x1x2 cell
with a different element, I would expect just such a xy--xz/yz
symmetry breaking as I am seeing in the trivial supercell.  But how
could I trust such a result if the symmetry is already broken just by
going to the larger cell?