[Pw_forum] Doubt in eigenvalues
Sohrab Ismail-Beigi
sohrab.ismail-beigi at yale.edu
Sat Jun 20 05:43:52 CEST 2009
> Message: 7
> Date: Fri, 19 Jun 2009 20:23:06 +0000 (GMT)
> From: Padmaja Patnaik <padmaja_patnaik at yahoo.co.uk>
> Subject: [Pw_forum] Doubt in eigenvalues
> To: pw_forum at pwscf.org
> Message-ID: <564271.86986.qm at web26105.mail.ukl.yahoo.com>
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>
> Dear all
>
> I am doing calculations on wide band gap semiconductor with a
> transition metal as impurity. Doing the scf calculations, DOS
> calculations, finding the magnetic moment etc. My problem comes
> while plotting the energy levels. What I expected that, the eigen
> values obtained should? indicate the splitting of levels into t2 and
> e sublevels. As t2 is 3 fold degenerate and e is two fold, so I
> expected that the eigen value which is repeated three times those
> corresponds to t2 and that repeated twice is for e. But the results
> obtained is quite confusing. I observe many sets of eigen values
> repeated twice and? thrice near the band gap region. I am performing
> calculations for both the spins. And this is happening for both
> spins. More than one set eigenvalues are found to be repeated twice
> and also thrice for the same K-point value. So how to know which one
> is the correct eigenvalue for t2 and e levels? Am i doing something
> wrong? I am looking at the dos output file
> for this plot.
> Can anybody please advise on this.
> Thanks in advance
>
> Regards
> Padmaja
>
> Padmaja Patnaik
>
> Research Scholar
>
> Dept of Physics
>
> IIT Bombay
>
> Mumbai, India
>
> ------------------------------
>
> Message: 8
> Date: Fri, 19 Jun 2009 16:33:38 -0400
> From: Nicola Marzari <marzari at MIT.EDU>
> Subject: Re: [Pw_forum] Doubt in eigenvalues
> To: PWSCF Forum <pw_forum at pwscf.org>
> Message-ID: <4A3BF622.2040507 at mit.edu>
> Content-Type: text/plain; charset=ISO-8859-1; format=flowed
>
>
> Dear Padmaja,
>
> 1) does the impurity give rise to isolated impurity levels ? If
> so, I presume you should plot band dispersions, and see flat bands.
> Then, you could plot the shape of the eigenstates at the Gamma point
> (or, if they are flat, indeed anywhere else), and see which ones look
> like the your eg or t2g
>
> 2) you could calculate the overlap between your states at gamma
> and the atomic d orbitals of you transition metal - this is done
> by the code when doing LDA+U calculations, so there should be
> an easy way (that I do not know) to print them out.
>
> 3) a more complex approach would be doing wannier postprocessing,
> to find out which are those impurity bands. note though that the
> localization procedure would probably give you random mixes of these
> orbitals, and you need an additional diagonalization step to recover
> the
> eg/t2g. This is explained in a M. Posternak et al Phys Rev B 2002.
>
> Any other suggestions ?
>
> nicola
>
>
> Padmaja Patnaik wrote:
>> Dear all
>>
>> I am doing calculations on wide band gap semiconductor with a
>> transition
>> metal as impurity. Doing the scf calculations, DOS calculations,
>> finding
>> the magnetic moment etc. My problem comes while plotting the energy
>> levels. What I expected that, the eigen values obtained should
>> indicate
>> the splitting of levels into t2 and e sublevels. As t2 is 3 fold
>> degenerate and e is two fold, so I expected that the eigen value
>> which
>> is repeated three times those corresponds to t2 and that repeated
>> twice
>> is for e. But the results obtained is quite confusing. I observe many
>> sets of eigen values repeated twice and thrice near the band gap
>> region. I am performing calculations for both the spins. And this is
>> happening for both spins. More than one set eigenvalues are found
>> to be
>> repeated twice and also thrice for the same K-point value. So how to
>> know which one is the correct eigenvalue for t2 and e levels? Am i
>> doing
>> something wrong? I am looking at the dos output file for this plot.
>> Can anybody please advise on this.
>> Thanks in advance
>>
>> Regards
>> Padmaja
>
>
> --
> ---------------------------------------------------------------------
> Prof Nicola Marzari Department of Materials Science and Engineering
> 13-5066 MIT 77 Massachusetts Avenue Cambridge MA 02139-4307 USA
> tel 617.4522758 fax 2586534 marzari at mit.edu http://quasiamore.mit.edu
>
>
> ------------------------------
>
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> End of Pw_forum Digest, Vol 24, Issue 43
> ****************************************
Dear Padmaja,
I think the first thing to do is to check point (1) of Nicola's reply
--- if you don't have relatively localized (i.e. weakly dispersive in
k-space) bands, then you don't have localized atomic-like states to it
makes little sense to talk of e2 versus t2g type orbitals to describe
the eigenstates.
Here is something relatively easy to try: compute atomic projected
densities of states. This is accomplished by the projwfc.x program
with appropriate input file (see help under INPUT_PROJWFC.txt or
something very similar depending on your version). What this means is
that for each atomic orbital defining your pseudopotential on each
atom of your system, the program computes the local density of states
versus energy projected onto that orbital (there are details on
orthogonalization which don't matter here).
You'd be mainly interested in looking at the local projected density
of states onto the d orbitals of the transition metal impurity. See
if there are large projections onto those orbitals in the vicinity of
the band gap or where you believe the states should be. Note that the
density of states is computed by projecting each eigenstate onto the
orbitals and then summing up all the contribtuions from all the
eigenstates, so if you use a narrow broadening, you can pick out
individual eigenstate peaks since you know their eigenenergies from
the output.
The program computes not only projections onto all the d-states of an
atom summed up but also onto the individual d orbitals (xy,xz,yz,3z^2-
r^2,x^2-y^2): assuming your system has some symmetry and you set up
your axes to be along those symmetry axes, this often means some of
these very orbitals are t2g and some are e2g --- you can then check to
see which particular ones have large projections at what energies.
The ordering has been documented and discussed in other parts of the
forum.
This would be a simple first step to get things going...
Best of luck,
---------------------------------------------
Sohrab Ismail-Beigi
Associate Professor of Applied Physics and Physics
Dept. of Applied Physics
Yale University
P.O. Box 208284
New Haven, CT 06520
Phone: 203.432.2107
Fax: 203.432.4283
Email: sohrab.ismail-beigi at yale.edu
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