Exciton wavefunction around fixed hole

[Franz Fischer]

Dear all,

I saw that you can use ypp to compute the electronic part of the exciton wavefunction around a hole fixed in r-space.
I saw in the code that you are computing it for a fixed exciton state \lambda this way:

rho_{re, rh=const.}^{\lambda} = |psi_{re,rh=const.}^{\lambda}|^2
= |\sum_{k vc} e^{ik(r_e - rh=const.)} u*_{vk}(rh=const.) u_{ck}(re) A_{kvc}^{\lambda}|^2

Can you tell me why hole part of the wavefunction is conjugated?
If I would write out the same equation naively, I would not get the same phase factor as you, rather e^{ik(r_e + rh=const.)}
and a non-conjugated u_{vk}(rh=const.) Bloch-part

Thanks in advance for your help.

Best,
Franz

[Daniele Varsano]

Dear Franz,

I'm not sure if I have understood your question,

excitonic wavefunction (phi) in real space is given by (omitting lambda):
phi(re,rh)=\sum_k\sum_cv A_cvk \psi_ck(re)\psi_vk(rh)*
see e.g. eq.50 in PRB 62, 4927 (2000), where psi_v/c are the valence and conduction Bloch function.

Can you elaborate more your doubt?

Best,
Daniele

[Franz Fischer]

Dear Daniele,

thanks for clarifying.
I did not know that it was defined like that and I also saw another paper (PRB 105, 115416 (2022) see eq. A19) that defines it without conjugation of the hole wavefunction that lead to my confusion.

Thanks again!

Best,
Franz