||The spin-splitting energy in wurtzite structure semiconductors had been investigated by linear combination of atomic orbital method (LCAO), atomic bond orbital method and two-band k•p method. In order to explain the large zero field spin splitting in wurtzite GaN, a different mechanism (ΔC1–ΔC3 coupling) was proposed, which originated from the intrinsic wurtzite effects (band folding and wurtzite bulk inversion asymmetry). The band-folding effect generates two conduction bands (ΔC1 and ΔC3), in which p-wave probability has tremendous change when kz approaches the anticrossing zone. The spin-splitting energy induced by theΔC1–ΔC3 coupling and wurtzite bulk inversion asymmetry is much larger than theory calculation of Kane model. When we apply the coupling to GaN/AlN quantum wells, we find that the spin-splitting energy is sensitively controllable by an electric field. |
It is also found that ideal wurtzite bulk inversion asymmetry yields not only a spin-degenerate line (along the kz axis; time reversal axis) but also a minimum-spin-splitting surface, which can be regarded as a spin-degenerate surface in the form of bkz2- k//2=0 (b≈4) near the Γ point. This phenomenon is referred to as the Dresselhaus effect (defined as the cubic-in-k term) in bulk wurtzite materials because it generates a term γwz(bkz2- k//2)(σxky-σykx)=0 in the two-band k•p Hamiltonian. And it is also demonstrated that in the k.p scheme, the spin splitting vanishes to cubic order in k. Consequently, the D’yakonov-Perel’ (DP) spin relaxation mechanism can be effectively suppressed for all spin components in  wurtzite quantum wells (QWs) at a resonance condition through device design with appropriate strain, gate voltage or optical illumination.
In conclusion: (1) the spin-splitting energy is enhance by wurtzite bulk inversion asymmetry; (2) the spin-splitting energy in wurtzite quantum well is sensitively controllable by electric field; (3) there exist a spin degenerate surface for wurtzite materials in k•p scheme. Therefore, wurtzite QWs (e.g., InGaN/AlGaN and InN/AlInN) are potential candidates for spintronic devices such as the resonant spin lifetime transistor.