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 |Mcv|2 (m-the number of valence band, n-the number of conduction band) along kx, ky, kzdirections 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= [(|M11-x|2)2+ (|M11-y|2)2 +(|M11-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, |Mcv|2= [(|Mcv-x|2)2+ (|Mcv-y|2)2 ]1/2 ?
For the extraordinary direction, |Mcv|2=|Mcv-z|2 ?
I have no idea about how to acquire the momentum matrix in a symmetric point like Gamma point. Could you give me some hints if you have some experience in it.
Thank you very much!
Best regards,
Jingjing
Felix-Bloch-Institut für Festkörperphysik
Halbleiterphysik
Linnéstraße 5
04103 Leipzig, Germany
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