Zero-field spin-splitting in Al$_{x}$Ga$_{1-x}$N/GaN heterostructures

We have observed the beating Shubnikov-de Haas oscillations with respect to the zero-field spin splitting of 2DEG in Al$_{x}$Ga$_{1-x}$N/GaN heterostructures. The spin-splitting energy was obtained about 9 meV from the beating SdH frequency derived by the non-linear curve fitting. A new mechanism ($\Delta _{C1}-\Delta _{C3}$ coupling) was proposed to describe the large spin splitting in wurtzite GaN, which is originated from the band folding effect and intrinsic wurtzite structure inversion asymmetry. The band-folding effect generates two conduction bands ($\Delta _{C1}$ and $\Delta _{C3})$, in which $p$-wave probability has tremendous change when $k_{z}$ approaches anti-crossing zone. The $\Delta _{C1}-\Delta _{C3}$ coupling can produce a spin-splitting energy much larger than traditional Rashba or Dresselhaus effects. This project is supported in parts by National Science Council, Core Facilities Laboratory in Kaohsiung-Pintung area, Taiwan (ROC).