Band decomposed charge density

[Dhirendra]

Hi,
I want to calculate the band decomposed charge density. For example, if I simulate silicon bulk using ATK-DFT then after that I want to calculate electron density (or charge density) in each valley of silicon (Delta and Gamma). I have checked this link http://quantumwise.com/forum/index.php?topic=1356.0 . But that is relevant for DeviceConfiguration. I have a BulkConfiguration. Is there anything similar for the bulk configuration?

 Also in the second comment (from Zh)
"The concept of the partial charge density of a given band or eigenvalue is basically the same as the local density of states.
http://quantumwise.com/documents/manuals/latest/ReferenceManual/index.html/ref.localdevicedensityofstates.html
The summing up the the local density of states for the eigenvalues at a specified band will give the band-decomposed partial charge density."
don't you think that just summing up ldos won't work in the conduction band. One has to sum up ldos x fermi function, no?

[Petr Khomyakov]

Please have a look at this forum post https://quantumwise.com/forum/index.php?topic=4962.msg21464#msg21464 on a similar topic.

[Dhirendra]

Thanks Petr,
I had gone through the posts. However, the approach is still not clear. I have few questions.
In the BlochState approach, the quantum_number argument to BlochState function is the band index, right? Can you please clarify.

I would also like to compare two approaches, 1) The BlochState approach and 2) The loca density of states approach, LDOS.

In the LDOS approach, if you follow second part of my opening comment, 'Zh' suggests that only summing up LDOS would give you band decomposed electron density. But I think LDOS x Fermi function to be summed up. Can you please clarify?

[Petr Khomyakov]

I guess you need to do integration of the DOS multiplied by the Fermi-Dirac distribution with respect to the energy from the bottom of the conduction band to infinity. But if your silicon is an intrinsic semiconductor, i.e., the Fermi level is in the middle of the band gap, the conduction band electron density will then be zero at 0 K, or rather small even at room temperature. I assume you are considering an n-type doped silicon.

[Dhirendra]

Thanks Petr for you reply. It satisfies my DOS query.

In the BlochState approach, I am wondering if the class BlochState has any method to return energy value of the quantum number it takes as an input. Quantum number is a band index right?

[Petr Khomyakov]

Yes, 'quantum_number' can be seen as a band index. Assuming that you have also calculated the band structure, you may then get the energies from the band structure, see the Bandstructure class description and useful notes in the reference manual at http://docs.quantumwise.com/manuals/Types/Bandstructure/Bandstructure.html.

[Dhirendra]

Thanks Petr.

Is the BlochState normalized?

[Dhirendra]

I need a precise definition of the BlochState. Is it only the envelope part of it?
psi_nk(r)=u_nk(r)exp(ik.r)

Is BlochState u_nk(r) ?

[Anders Blom]

BlochState is u_nk but when we plot it in VNL we also include the phase factor, so there we plot psi.