Optical transition matrix elements

[Rui Emanuel Ferreira da Silva]

Hello,

Is there any way with Elk to get the Optical transition matrix? Explicitly the matrix is defined as
$\xi_{nm}(k)=\int u_{nk}^{}\left(r\right)\nabla_{k}u_{mk}\left(r\right)dr $*, see PHYSICAL REVIEW B 76, eq 4, 035213 2007. I have seen that the code calculates the momentum matrix elements but I am interested also in the terms n=m, the Berry connection terms.

Kind regards,
Rui

[Sangeeta Sharma]

Hi

The momentum matrix elements are calculated in routine genpmatk.f90. You can slightly change this routine and put a write statement to get the required elements.

Best
sharma

[mfechner]

Dear Sanngeeta,

sorry for bothering with my bad knowledge of optical tranistions but

are the momentum matrix elements gradient with respect to r
the same as the optical transiton matrix elements asked above defined
by the gradient of k ?

best regards
Michael

[Rui Emanuel Ferreira da Silva]

Hi Sharma,

I was aware that ELK can calculate the momentum matrix elements. But I am interested in the berry connections. These are the dipole couplings between the same bloch function and not the momentum matrix elements. See eq. 4 at PHYSICAL REVIEW B 76, 035213 2007.

Best
Rui

[Sangeeta Sharma]

Hi Rui,

My student Mr. Chung-Yu Wang is implementing this at the moment. You can contact him and see when he can give you the routines etc. email: cywang@mpi-halle.mpg.de

Best