[Wien] lapw5

[Lukasz Plucinski]

It seems gmail did not send my last email, so I am trying again:

Dear All,

A bit more information on my lapw7 issue.

First of all, my degenerate states are not orthogonal. Perhaps their linear
combinations are.

I calculate charge density for a particular k and a particular state
number. I work with a symmetric slab of the 1T TMDC lattice. For a surface
state, this means that what is spin-up on side A of the slab should be
spin-dn on side B of the slab, |Psi_k_A(r)| = |Psi_k_B(-r)| (sides A and B
are symmetric, r=0 is e.g. in the middle of the slab).

Now, I have 2 degenerate eigenvalues at some energy, in my case e.g.
eigenvalue #1461 and #1462. In principle one of them should host spin-up
state on side A of the slab, and the other should host spin-dn state at
side B of the slab. However, this is not the case, and the charge of the
surface states is shared by the eigenvalues (this also makes the states
non-orthogonal).

lapw7 can calculate the full wave function with the phase. Now the
following DOES NOT hold:

NOT TRUE: |Psi_k_#1461_A_up(r) + Psi_k_#1462_A_up(r)| =
|Psi_k_#1461_B_up(-r) + Psi_k_#1462_B_up(-r)|

But the following holds:

TRUE: |Psi_k_#1461_A_up(r) + Psi_k_#1462_A_up(r)| = |Psi_k_#1461_B_up(-r)
- Psi_k_#1462_B_up(-r)|

This means that the spin-dn wave functions need to be added out-of-phase to
obtain what is expected. Actually, from the 2D plot of the phase of Psi one
can see that, for the two degenerate eigenvalues, spin-up wave functions
are in-phase, and spin-dn wave functions are out-of-phase.

Can you comment and advise how to deal with that?

Best,
Lukasz
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