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<font face="Calibri">Dear Seunghwan,<br>
<br>
In general, the MLWFs correspond to a transformation of a <i>set</i>
of energy bands (determined by the energy windows that one defines).
Unless a particular band is isolated from the rest of the bands in the
Brillouin zone, which can happen, for example, when you have a very
localised defect level, no single particular MLWF will correspond
directly to a single particular band. <br>
<br>
Let us for a moment assume, for simplicity, </font><font face="Calibri">Gamma-point
only sampling of the BZ and that we don't need to do any
disentanglement procedure.</font><font face="Calibri"> One may want to
know how much "character" of a particular energy eigenstate $\psi_{n}$
is present in a particular MLWF $w_{m}$ (or vice versa). Then one
should look at the quantity $|< \psi_{n} | w_{m} >|^2$. If you
work it out, this is just $|U_{nm}|^2$ where U is the matrix in Eq.
(10) of Marzari & Vanderbilt, <i>Phys Rev B</i> <b>56</b>, 12847
(1997) [or, alternatively, Eq. (1) of <i>Comput Phys Commun</i> <b>178</b>,
685 (2008)]. Mathematically, this is just the square of the projection
of the eigenstate on the MLWF, and gives a measure of the amount of
overlap between them.<br>
<br>
Hope that helps.<br>
<br>
Arash<br>
<br>
</font>
<pre class="moz-signature" cols="72">--
Dr Arash A Mostofi
Lecturer and RCUK Fellow
Depts of Materials & Physics
Imperial College London
London SW7 2AZ, United Kingdom
T +44 (0)207 594 8154
F +44 (0)207 594 6757
E <a class="moz-txt-link-abbreviated" href="mailto:a.mostofi@imperial.ac.uk">a.mostofi@imperial.ac.uk</a>
W <a class="moz-txt-link-freetext" href="http://www.cmth.ph.ic.ac.uk/people/a.mostofi">http://www.cmth.ph.ic.ac.uk/people/a.mostofi</a>
</pre>
<br>
<br>
seunghwan lee wrote:
<blockquote cite="mid:883705.99470.qm@web50508.mail.re2.yahoo.com"
type="cite">
<pre wrap="">Hi All,
I have a question about plotting Wannier orbitals. The question may
not make any sense, but is there any way to relate a particular
wannier orbital and an energy band? For example, if I want to plot
the HOMO and LUMO of a semi-conducting system, is it possible to find
these orbitals from the set of MLWO calculated with W90?
Thank you for your help.
Seunghwan Lee
University of North Carolina
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