Question

What do we get from the diagonalization of the $k\cdot p$ matrix?

Answer 1

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What do we get from the diagonalization of the k⋅pk⋅p matrix?

solid-state-physics electronic-band-theory approximations

In k.p theory, we expand the wave function around a known point k0k0

uλ(k)=∑νcλ,ν(k)uν(k0).uλ(k)=∑νcλ,ν(k)uν(k0).

If we now consider 8 bands (conduction, heavy-hole, light-hole, split-off, each twice spin degenerate), over what states do we have to sum up? Would it the 8 bands or is the spin not included here and it is only 4 bands?

If we now solve the 8x8 k.p Hamiltonian for one point in momentum space, we get 8 eigenvalues and 8 eigenvectors of length 8. I want to make sure that I understand the connection to physics correctly: The 8 eigenvalues are the band energies of the 8 bands for that particular momentum. The 8 eigenvectors each have 8 entries which are the coefficients cλ,νcλ,ν. Is that correct?