Dear Lukasz,
Wannier basis is pretty similar to TB basis, but they are not fully equivalent.
In Wannier basis Hamiltonian contributions from quite distant neighbors are
important, they are not automatically localized on atoms, have proper symmetry,
etc.
I recommend to check the following papers where proper TB is constructed from
the Wannier functions:
https://doi.org/10.1103/PhysRevB.92.085301
https://doi.org/10.1103/PhysRevMaterials.2.103805
https://doi.org/10.1103/PhysRevB.99.125117
Sincerely yours,
Mikhail
>Четверг, 15 февраля 2024, 1:41 +01:00 от 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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