[Wien] Wannier

[pluto]

Dear Oleg, Mikhail, dear Prof. Blaha,

Thank you for the quick answers!

It seems that the Alm (related to the "u") coefficient might be what I 
need, because it refers to the "atomic-like" potential. Perhaps the Blm 
coefficient, related to the "u-dot", is "small" in most cases, also 
maybe it somehow represents the non-atomic (i.e. non-LCAO) correction to 
the electronic state inside the MT sphere? I apologize if calling "u" of 
LAPW as being "atomic" is wrong, but maybe it is not totally wrong in 
the spirit of my problem. I am fine with approximate numbers here, 
everything in the order of 80%-90% (say referring to the final ARPES 
intensity) would be fine, I think. (The Alm of different atoms would 
just control the amplitude and phase interference of the spherical waves 
photoemitted from these atoms.)

Does that way of thinking make some sense?

Perhaps it is also the case, that a very large LCAO basis can explain 
any band structure, but I think this is not the point, here the goal is 
to simplify the problem.

In this physical problem, I cannot live without the complex 
coefficients. This is easily understood in graphene, where the "dark 
corridor" of ARPES results from the k-dependent phases of the 
wave-functions on sites A and B.

Best,
Lukasz


On 2024-02-15 08:40, Peter Blaha wrote:
> Hi,
> I do not know too much about Wannerization and LCAO models.
> 
> However, I'd like to mention the  PES  program, which is included in 
> WIEN2k.
> 
> It uses the atomic cross sections (as you mentioned), but not the
> wavefunctions, but the "renormalized" partial DOS. (This will omitt
> the interstital and renormalize in particular the delocalized
> orbitals).
> 
> It does NOT include  phases (interference), but our experience is
> quite good - although limited. Check out the PES section in the UG and
> the corresponding paper by Bagheri&Blaha.
> 
> Regards
> 
> Am 15.02.2024 um 01:41 schrieb pluto via Wien:
>> 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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