[Wannier] plotting Wannier orbitals

seunghwan lee seung43210 at yahoo.com
Mon May 10 17:21:43 CEST 2010

Dr. Mostofi,

Thank you for your kind comments. Is there any way to find this rotation matrix U_mn? I see .anm and .mmn files from W90 output, but not .umn

Seunghwan Lee
University of North Carolina

--- On Sat, 5/8/10, Arash Mostofi <a.mostofi at imperial.ac.uk> wrote:

From: Arash Mostofi <a.mostofi at imperial.ac.uk>
Subject: Re: [Wannier] plotting Wannier orbitals
To: "wannier at quantum-espresso.org" <wannier at quantum-espresso.org>
Date: Saturday, May 8, 2010, 1:22 PM

Dear Seunghwan,

In general, the MLWFs correspond to a transformation of a set
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. 

Let us for a moment assume, for simplicity, Gamma-point
only sampling of the BZ and that we don't need to do any
disentanglement procedure. 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, Phys Rev B 56, 12847
(1997) [or, alternatively, Eq. (1) of Comput Phys Commun 178,
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.

Hope that helps.


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.mostofi at imperial.ac.uk
W  http://www.cmth.ph.ic.ac.uk/people/a.mostofi

seunghwan lee wrote:

  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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