Symmetry in Indirect exciton in presence of phonons

[sitangshu]

Dear developers,

I have a 2D hexagonal crystal with C3v (3m) point group in which I am studying the PL emission. I realised that the Q=0 exciton has E-type symmetry.
I noticed that the indirect (lowest) exciton is located between K-\Gamma of the exciton dispersion. The phonon transferred momenta (q) is between \Gamma-M, where the symmetry is C_s(m). From the character table of C3v(m) and C_s(m), I could find the C3 axis of C3v (3m) is equivalent to mirror axis (\sigma) in C_s(m). However, I am not able to understand the "Wonderful Orthogonality Theorem" in this case from Dresselhaus book, which can tell me about the information about the dipole operation as discussed in Phonon assisted spectra of hBN: https://journals.aps.org/prb/abstract/1 ... .99.081109
Note that, in the phonon assisted DOS (https://www.yambo-code.eu/wiki/index.ph ... emperature), I am getting phonon replicas with finite contribution from out of plane phonon modes (both ZA and ZO).
For D_6h case ZO is zero, but is it true for all?
Can anyone suggest this issue?

Regards,
Sitangshu