Probing the cubic crystal anisotropy and spin-orbit interaction in GaAs heterostructures using hole quantum point contacts

Understanding the form of the spin-orbit interaction (SOI) in semiconductors such as GaAs is a prerequisite for engineering of topological superconducting and insulating states in these materials. Zeeman spin-splitting transport measurements in p-type 1D quantum point contacts (QPCs) are an effective probe of the SOI. Previous measurements have shown that there is a strong anisotropy in the in-plane g-factors in hole QPCs due to SOI (g_||I > g⊥I), which can be explained as arising from a second k⁴B Zeeman term in addition to the established k²B Zeeman term¹.

Here we present the first study of the effect of cubic crystal anistropies on the anisotropy of the g-factor. By rotating the QPC with respect to the crystal axes, we change the effect of the cubic crystal terms. We find the anisotropy of the g-factor is strongly dependent on QPC orientation, and present a theoretical framework describing the SOI terms arising from cubic crystal anisotropy. We identify four additional Zeeman terms that describe the dependence of the anisotropy of the in-plane g-factors with respect to QPC orientation. Our model shows that SOI is highly dependent on crystal asymmetries with implications for topological systems such as artificial graphene.

¹Miserev et al., Phys. Rev. Lett. 119 116803 (2017)