Spin-orbit coupling in GaN/AlGaN wurtzite quantum wells*

We investigate the spin-orbit coupling for electrons in wurtzite quantum wells with two subbands [1]. By folding down the 8$\times $8 Kane model, accounting for the s-pz orbital mixing [2, 3] absent in zincblende structures, we derive an effective 2$\times $2 Hamiltonian for the conduction electrons. In this derivation we consider the renormalization of the spinor component of the conduction band wave function, which is crucial to properly obtain the corresponding spin-orbit couplings. In addition to the Rashba-type term arising from the bulk inversion asymmetry of the wurtzite lattice, we obtain the usual linear in momentum Rashba term induced by the structural inversion asymmetry of the well and; interestingly, we also find a new Rashba-like contribution. The spin-orbit coupling parameters are obtained via a self-consistent calculation. For completeness, the Dresselhaus term is also included in our calculation. \\[4pt] [1] Rafael S. Calsaverini, Esmerindo Bernardes, J. Carlos Egues, and Daniel Loss, Phys. Rev. B 78, 155313 (2008). \\[0pt] [2] L. C. Lew Yan Voon, M. Willatzen, and M. Cardona, Phys. Rev. B 53, 10703 (1996). \\[0pt] [3] J. Y. Fu and M. W. Wu, J. Appl. Phys 104, 093712 (2008).