[QE-users] how to obtain the transition matrix elements of momentum operator

[jy95vowa]

Hi everyone,

  I have some questions about calculating the transition matrix elements of the momentum operator between the valence and conduction bands in quantum espresso.

 

 I know that in the file of p_avg.dat, there are three matrixs of m × n entries |M_cv|² (m-the number of valence band, n-the number of conduction band) along kx, ky, kz directions for every chosen k point.

So for the materials with cubic crystal structure (isotropic), is the transition matrix elements from first valence band to first  conduction band is obtained directly by the equation |M₁₁|²= [(|M_11-x|²)²+ (|M_11-y|²)² +(|M_11-z|²) ² ]^1/2 ?

 

For materials with anisotropic rhombohedral crystal structure for example, the transition matrix elements is composed of two parts along the ordinary (perpendicular to the c axis) and extraordinary direction (parallel to the c axis), how can I get the different transition matrix elements along two different  directions?

                                For the ordinary direction, |M_cv|²= [(|M_cv-x|²)²+ (|M_cv-y|²)² ]^1/2  ?

                                For the extraordinary direction, |M_cv|²=|M_cv-z|² ?

 

Any reply is appreciated! Thank you very much!

 

 Best regards,

 Jingjing

 

 

 

--

M.Sc. Jingjing Yu

Universität Leipzig
Felix-Bloch-Institut für Festkörperphysik
Halbleiterphysik
Linnéstraße 5
04103 Leipzig, Germany

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