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I am interested in knowing the electrostatic potential in specific regions of the Brillouin zone of an ab initio calculation where an external electric field was applied to a bilayer system perpendicularly. The intention is to calculate the potential drop the system sees for those specific states of interest. I am using QE for the calculations. I saw that pp.x offers the electrostatic potential for the entirety of the system. However, I am not sure how helpful would be in this case as the effect I study occurs around one symmetry point of the upper valence band, and the charge distribution over the whole momentum space for that energy level behaves quite differently under the applied electric field.

Is there any way to extract the electrostatic potential per energy state and kpoint?

In case is relevant, I am used to working with the wavefunctions files, but I am not sure in what way the electrostatic potential is calculated by QE (I am not so experienced with Fortran) in case the only way is calculating it manually.

Thank you for your time.

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    $\begingroup$ The Brillouin zone is a mathematical artifact that allows us to calculate electronic properties of periodic systems in the inverse/reciprocal space, it is not a "real" thing. On the other hand, the electrostatic potential is a real property calculated in the 3D direct space that depends on the charge distribution. I am afraid that what you want is not possible. $\endgroup$
    – Camps
    Commented Aug 27 at 12:50
  • $\begingroup$ @Camps Thanks a lot for your quick and nice answer. Wouldn't it be possible though, to quantitatively determine how much of the charge on a specific state has been shifted towards one layer under an external field? I thought a potential drop would be a good descriptor. $\endgroup$
    – MicMC
    Commented Aug 27 at 13:26
  • $\begingroup$ "towards one layer" is a thing you say in position space. That does not exist in Brillouin zone. $\endgroup$ Commented Aug 27 at 14:42
  • $\begingroup$ @naturallyInconsistent I see your point. How can one describe then the charge transfer of electrons of specific momentum under a perturbation? What I see, is that to the layer net charge transfer some orbitals in one layer are depleted while others accumulate more charge. Others follow the opposite trend. $\endgroup$
    – MicMC
    Commented Aug 27 at 15:44
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    $\begingroup$ You always can run two calculations (with/without electric field) and compare any properties you want for both calculations. $\endgroup$
    – Camps
    Commented Aug 27 at 16:51

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