[QE-developers] Problem of the momentum matrix element at the Gamma point

[L Y]

Dear Quantum ESPRESSO developers,

My question was posted initially to the user mail list, and I already
obtained help from Dr. Iurii. It is abit technical, so I formulate it here
again to see if anyone has ideas or suggestions. I think it could be a bug.

I calculated the the momentum matrix element between the valence and
conduction bands in MgO, along a k-path going through the Gamma point. At
the Gamma point, there is a clear discontinuity, see attachment
"p_with_nonlocal.png" (Gamma point at ik=31), while the band energies are
all continuous. I tried many different types of pseudopotentials (norm
conserving, ultrasoft, PAW) and functionals (LDA, PBE), all showing this
discontinuity, (although the SG15 ONCV pseudopotentials seem to be better).

When I commented out the part in "compute_ppsi.f90" involving the non-local
pseudopotential, the discontinuity is gone, see attached
"p_without_nonlocal.png". This leads me to believe that there is
potentially a bug in the calculation of the commutator i [r, V_nl] for the
Gamma point. I was wondering whether anyone has ideas or suggestions on why
this occurs and where in the code I should look at to try to find the
potential "bug".

Sorry for the long mail.
Best regards,
Lun Yue
Louisiana State University
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