[Wannier] Expanding wannier Hamiltonian of the unit cell to that of the supercell

[Stepan Tsirkin]

Dear Kenan,


the Wannier Hamiltonian that you get is a num_wann x num_wann matrix 
H_mn(R) which depends on an R vector, which means that the hopping 
connects orbital nin unit cell 0 to the orbital m in unit cell R (or 
exchange indices n,m, not sure).  In a supercell the same matrix would 
correspond to connceting primitive cells R' and R'+R (where R' runs over 
all 10000 primitive cells in oyur supercell)

Such things are implemented, for instance , in pythTB 
http://www.physics.rutgers.edu/pythtb/ package, (which however may be 
very slow, but you may look to have an idea)

Also Wanniertools http://www.wanniertools.com/ may be useful.

Regards,

Stepan Tsirkin,
University of Zurich.

P.S. (I think it is a rule of this mailing list to specify your 
affiliation )

On 28.01.21 08:07, Kenan Song wrote:
> Dear All,
>
> I extracted the wannier Hamiltonian for a 2D system after the 
> wannierization is done. Now, I want to expand this wannier Hamiltonian 
> to that for the supercell (e.g. 100 by 100) of the original 2D system.
>
> Can I just copy the wannier Hamiltonian of the original 2D system and 
> paste it onto the diagonal part in the supercell Hamiltonian matrix 
> 10000 times?
>
> If so, would anyone please tell me how to deal with the off-diagonal 
> part in the supercell Hamiltonian matrix?
>
> Would anyone please tell me how to account the hopping between 
> different atoms in different neighbour unit cells?
>
> Would anyone please recommend some solutions or reference papers, 
> discussing the expansion of the wannier Hamiltonian?
>
> Thank you all very much in advance.
>
> Kind regards,
>
> Kenan Song
>
> ------------------------------------------------------------------------
> This message and its contents, including attachments are intended 
> solely for the original recipient. If you are not the intended 
> recipient or have received this message in error, please notify me 
> immediately and delete this message from your computer system. Any 
> unauthorized use or distribution is prohibited. Please consider the 
> environment before printing this email.
>
> _______________________________________________
> Wannier mailing list
> Wannier at lists.quantum-espresso.org
> https://lists.quantum-espresso.org/mailman/listinfo/wannier
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.quantum-espresso.org/pipermail/wannier/attachments/20210128/df61b235/attachment.html>