Spin-orbit coupling: atom versus semiconductor crystal

Abstract

We reconsider a key point in semiconductor physics, the splitting of the valence band states induced by the spin-orbit interaction, through a novel approach which uses neither the group theory formalism, nor the usual $\text{L}\cdot \text{S}$ formulation valid for atoms but conceptually incorrect for periodic lattices, the angular momenta $\text{L}$ and $\text{J}$ having no meaning due to the absence of spherical symmetry. We show that for zinc-blende structures, the valence band eigenstates resulting from spin-orbit coupling are uniquely determined by: (i) the equivalence of the ($x,y,z$) crystal axes, (ii) the three-fold degeneracy of the valence band. The fact that these two conditions are also fulfilled by atomic $p$ states allows us to understand why the spin-orbit eigenstates for three-fold atomic and valence electrons have exactly the same structure, albeit the drastic differences in the potential and electronic symmetries. We also come back to the commonly accepted understanding of the exciton-photon interaction in terms of bright and dark excitons having total angular momenta $J=(1,2)$ respectively and present a simple derivation of this interaction which only relies on spin conservation.

References in corpus (1)

• Three-band tight-binding model for monolayers of group-VIB transition metal dichalcogenides

Cited by in corpus (6)

• Optical signature of quantum coherence in fully dark exciton condensates
• Understanding Semiconductor Valence Mass
• Missing understanding of the phase factor between valence-electron and hole operators
• Exploring the change of semiconductor hole mass under Coulomb scattering
• Photocreation of a dark electron-hole pair in a quantum dot
• From spherical to periodic symmetry: the analog of orbital angular momentum for semiconductor crystals