Talk:Luttinger–Kohn model

1. Did anybody notice the different signs of the basis functions u_10 to u_80 used in this article? I think it is different from what is used else where in the literature, even if the literature is not so consistent. Is it correct here?

212.139.202.21 (talk) 05:04, 14 March 2011 (UTC)The phase factor (sign in this case) is a matter of choice. However, the basis function given is that of Γ_8^- irreducible representation of the symmetry group O_h. To use it for zincblende crystal (as is the case for Luttinger & Kohn), a unitary transformation is required which changes the order of the light hole and heavy hole states. The conduction band symmetry then need to change as well to maintain agreement with experimental observation of selection rules for optical transitions. Forthcoming article in PRB deals with this and other errors in the current k.p method based on single group consideration.

2. Does anybody know, what E0 in the denominator of U is in the application of the Lödwin's perturbation method to the Hamiltonian with spin-orbit coupling? For the general case considered first, it seems that the E in the denominator is the full band of a chosen band and that this simply gets exchanged by E0???? Can someone expand this to make some sense?? Thanks!

212.139.202.21 (talk) 05:04, 14 March 2011 (UTC)As an approximation, one substitute the un-perturbed energy of the band in place of E. Under single group formulation, there is no allowance of spin splitting of the un-perturbed state even when the basis include spin degree of freedom. (There is a spin dependent perturbation term which exist at k=0 as well). When dealing with inter-band Lowdin terms, average of 1/(E_1-E_\gamma) and 1/(E_2-E_\gamma) can be used.

Error in Hamiltonian

Explicit matrix of the 8x8 band Luttinger-Kohn Hamiltonian is incorrect. 145.90.38.238 (talk) 17:28, 19 June 2023 (UTC)

Can you fix it or cite a source?--ReyHahn (talk) 09:52, 20 June 2023 (UTC)