Question

I've been reading about the Kane-Mele model and noticed that it does not include nearest-neighbor spin-orbit coupling, with explanations often pointing to mirror symmetry as the reason. Could someone explain why mirror symmetry in the model leads to the exclusion of nearest-neighbor spin-orbit coupling? I assume, in the Kane-mele model, the basis is the pz

orbitals which are perpendicular to the 2D plane. Considering this, I think the spin-orbit coupling matrix elements shall not differ much between nearest-neighbor and next-nearest-neighour.

Answer 1

Mirror symmetry in the Kane-Mele model excludes nearest-neighbor spin-orbit coupling due to its effect on the energy levels of electrons.

Step-by-step explanation:

Mirror symmetry in the Kane-Mele model leads to the exclusion of nearest-neighbor spin-orbit coupling because it affects the energy levels of the electrons. In this model, the spin-orbit coupling is negligible for nearest-neighbor interactions due to mirror symmetry, but it becomes significant for next-nearest-neighbor interactions. Mirror symmetry restricts the interactions between certain orbitals, resulting in the exclusion of nearest-neighbor spin-orbit coupling. On the other hand, next-nearest-neighbor interactions can still occur due to the lack of mirror symmetry between those orbitals.