I am trying to set up a k.p (k dot p) calculation to get the band structure and expansion coefficients of a bulk semiconductor (such as GaAs or InSb). The Hamiltonian I use can be found in this paper (Phys. Rev. B 55, 6960 (1997)) and includes conduction, heavy-hole, light-hole, split-off bands, each twice spin degenerate. When I diagonalize the Hamiltonian, I get the same band structure (eigenvalues) as in the paper, so I am confident that I did it correctly. However, I am also interested in the expansion coefficients (eigenvectors) to compute Coulomb and dipole matrix elements. After sorting eigenvalues (and eigenvectors accordingly) in decreasing order, I am left with the problem that I cannot match the eigenvectors and eigenvalues uniquely to one band, since they are degenerate. That means that after sorting, I end up mixing these 2 degenerate bands. I had success bypassing this issue by adding a small energy to one of the degenerate bands (meaning that I added a small energy on the diagonal of the Hamiltonian). But, while my choice of adding the energies (which can be positive or negative) works in one direction (Gamma-X), the 2 now not-degenerate bands cross each other and then my sorting fails (see the figures I attached). My question is: How can I distinguish the 2 degenerate bands I get from a k.p calculation? Is there a smart way to do this?
check if this link could help you http://xxx.tau.ac.il/abs/1410.4993
if so I can send you the full thesis file for more information.
No, this actually doesn't help. As far as I understand your paper, you do not state how you numerically distinguish the coefficients of the bands with degenerate energy. There is just the statement that the coefficients follow from the diagonalization. The problem is that each energy band is twice degenerate and I am searching for a way to not mix these degenerate bands. Or did I read over something?
The origin of degeneracy is spin and you will come over it while calculating Coulomb coupling. In fact I have used the same radial part of the wavefunction for degenerate bands but using spherical harmonics for the spherical part will bring the spin in the calculation. I am not sure if this explanation could help.
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