[QE-users] Wavefunction Overlap for Different K-space Samplings

[Nielsen, Carl Emil]

[wf.png]

Hi,

I’m currently computing wave function overlap of some KS-wave functions produced by QE for monolayer MoS2 with SOC enabled. The wave functions are read with HDF5 in Fortran. However, something is bothering me. When computing

< nk | nk’ >,

for k = (0.0 , 0.0 , 0.0) and k’ = (1/3, 1/3, 0) in crystal coordinates, and some fixed band, n (I choose the top valence band in this example), I get wildly different values depending on the k-space sampling. I’ve attached a figure, displaying the absolute value of < nk | nk’ > for different k-space samplings.

I would have imagined, that the values of < nk | nk’ > should either be identical or at least look smooth when plotted against the k-space sampling. Can you clarify on this behaviour?

As a note, the wave function stored in your .hdf5 files have four times the length of the number of planewaves (npw). Therefore, I rearrange the wave function as (Fortran version)

psi_up_r = psi_k(1        :npw_   ,:),
psi_up_i = psi_k(npw_+1   :2*npw_ ,:),
psi_dw_r = psi_k(2*npw_+1 :3*npw_ ,:),
psi_dw_i = psi_k(3*npw_+1 :4*npw_ ,:),

where r denotes the real part and vice versa for i. Moreover, I am aware that the G-basis varies for each k-point, and I took care of this as well.

Kind regards

Carl Emil Mørch Nielsen

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MSc. Carl Emil Mørch Nielsen
Universität Hamburg
HARBOR, Geb. 610
Luruper Chaussee 149
D-22761 Hamburg
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