[Wien] Wannier

[Rubel, Oleg]

Dear Lukasz,

Let me try to address the Wannier part of your question. There is a tutorial on construction of maximally localized Wannier functions for GaAs with WIEN2k+w2w+wannier90. Please check one of the latest workshops at http://susi.theochem.tuwien.ac.at/events/index.html. In this tutorial, you will see a nice analogy with the sp3 LCAO model. This is because we got lucky, and the Wannier functions ended up centered at the atomic sites. However, this is not generally the case, even though you can initially place WFs at the atomic sites. Simple Si is an example where the centers of WFs stray away from the centers of atoms. In any case, we technically obtain a TB Hamiltonian that fits the band structure, but the LCAO interpretation (atomic orbitals) is not possible in most cases. (At least, this has been my experience.)

There are developments beyond "standard" wannierization, for instance, symmetry-constrained WFs. There was a good summer school on Wannier90 (https://indico.ictp.it/event/9789/), so please check the program. I do not know if those developments allow for constraining the centers of WFs. I recall that symmetry-constrained WFs require additional input that is not automatically generated by WIEN2k.

If you find a solution on how to get an LCAO Hamiltonian for a generic material, please post it to the list.

Thank you in advance
Oleg

--
Oleg Rubel (PhD, PEng)
Department of Materials Science and Engineering
McMaster University
Web: http://olegrubel.mcmaster.ca



> -----Original Message-----
> From: Wien <wien-bounces at zeus.theochem.tuwien.ac.at> On Behalf Of pluto
> via Wien
> Sent: Wednesday, February 14, 2024 7:41 PM
> To: A Mailing list for WIEN2k users <wien at zeus.theochem.tuwien.ac.at>
> Cc: pluto <pluto at physics.ucdavis.edu>
> Subject: [Wien] Wannier
> 
> Caution: External email.
> 
> 
> Dear All,
> 
> I am interested to project WIEN2k band structure onto atomic orbitals, but
> getting complex amplitudes. For example, for graphene Dirac band (formed
> primarily by C 2pz) I would get two k-dependent complex numbers
> A_C2pz(k) and B_C2pz(k), where A and B are the two inequivalent sites, and
> these coefficients for other orbitals (near the Dirac points) would be nearly
> zero. Of course, for graphene I can write a TB model and get these numbers,
> but already for WSe2 monolayer TB model has several bands (TB models for
> WSe2 are published but implementing would be time-consuming), and for a
> generic material there is often no simple TB model.
> 
> Some time ago I looked at the WIEN2k wave functions, but because of the
> way LAPW works, it is not a trivial task to project these onto atomic orbitals.
> This is due to the radial wave functions, each one receiving its own coefficient.
> 
> I was wondering if I can somehow get such projection automatically using
> Wien2Wannier, and later with some Wannier program. I thought it is good to
> ask before I invest any time into this.
> 
> And I would need it with spin, because I am interested with systems where
> SOC plays a role.
> 
> The reason I ask:
> Simple model of photoemission can be made by assuming coherent addition
> of atomic-like photoionization, with additional k-dependent initial band
> amplitudes/phases. One can assume that radial integrals in photoemission
> matrix elements don't have special structure and maybe just take atomic cross
> sections of Yeh-Lindau. But one still needs these complex coefficients to allow
> for interference of the emission from different sites within the unit cell. I think
> for a relatively simple material such as WSe2 monolayer, the qualitative result
> of this might be reasonable. I am not aiming at anything quantitative since we
> have one-step-model codes for quantitative.
> 
> Any suggestion on how to do this projection (even approximately) within the
> realm of WIEN2k would be welcome.
> 
> Best,
> Lukasz
> 
> 
> PD Dr. Lukasz Plucinski
> Group Leader, FZJ PGI-6
> Phone: +49 2461 61 6684
> https://electronic-structure.fz-juelich.de/
> 
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