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<p>Dear Kenan,</p>
<div class="moz-cite-prefix"><br>
</div>
<div class="moz-cite-prefix">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)</div>
<div class="moz-cite-prefix"><br>
</div>
<div class="moz-cite-prefix">Such things are implemented, for
instance , in pythTB <a class="moz-txt-link-freetext" href="http://www.physics.rutgers.edu/pythtb/">http://www.physics.rutgers.edu/pythtb/</a>
package, (which however may be very slow, but you may look to have
an idea)</div>
<div class="moz-cite-prefix"><br>
</div>
<div class="moz-cite-prefix">Also Wanniertools
<a class="moz-txt-link-freetext" href="http://www.wanniertools.com/">http://www.wanniertools.com/</a> may be useful.</div>
<div class="moz-cite-prefix"><br>
</div>
<div class="moz-cite-prefix">Regards,</div>
<div class="moz-cite-prefix"><br>
</div>
<div class="moz-cite-prefix">Stepan Tsirkin,</div>
<div class="moz-cite-prefix">University of Zurich.</div>
<div class="moz-cite-prefix"><br>
</div>
<div class="moz-cite-prefix">P.S. (I think it is a rule of this
mailing list to specify your affiliation )<br>
</div>
<div class="moz-cite-prefix"><br>
</div>
<div class="moz-cite-prefix">On 28.01.21 08:07, Kenan Song wrote:<br>
</div>
<blockquote type="cite"
cite="mid:CAMbJXZ_+0tSsboopaonHaWnUCbs5NK8fEGrptXg2nmfjWEBDMA@mail.gmail.com">
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<div>Dear All,</div>
<div><br>
</div>
<div>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.</div>
<div><br>
</div>
<div>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?</div>
<div><br>
</div>
<div>If so, would anyone please tell me how to deal with the
off-diagonal part in the supercell Hamiltonian matrix?</div>
<div><br>
</div>
<div>Would anyone please tell me how to account the hopping
between different atoms in different neighbour unit cells?</div>
<div><br>
</div>
<div>Would anyone please recommend some solutions or reference
papers, discussing the expansion of the wannier Hamiltonian?<br>
</div>
<div><br>
</div>
<div>Thank you all very much in advance.</div>
<div><br>
</div>
<div>Kind regards,</div>
<div><br>
</div>
<div>Kenan Song<br>
</div>
</div>
<br>
<div>
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<pre class="moz-quote-pre" wrap="">_______________________________________________
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</pre>
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