K.P method for valence band

[SolitaryWalkerX]

Homework Statement

As the attached file, I have no idea for dealing with this problem.

My professor just taught the non-degenerate version of k.p method , and it seems not working

here because the denominator would go to infinity for the degenerate states.

I've read through some materials (degenerate kp method, Kane Model,

Luttinger–Kohn model, etc.), but I found I can't simply apply degenerate kp method here since

the band split into a singlet and a doublet. Besides, although Kane's 3 Bands or 4 Bands model

seems highly related[1], the result(energy dispersion) of 4 bands model is a bit weird

(3 Bands Model is beyond my knowledge, e.g., DKK Hamiltonian and IRR).

As for Luttinger–Kohn model, it goes way too far.

Overall, I just want to know how should I solve this kp method Problem.

Especially, how can I cope with the degenerate states and the siglet/doublet band?

Thanks

Relevant Equations

[1]https://web.wpi.edu/Pubs/ETD/Available/etd-120905-095359/unrestricted/cgaleriu.pdf

 

[Nate810]

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