Mapping the anisotropy of the Zeeman spin splitting of one-dimensional heavy holes in a GaAs quantum point contact

We have studied the anisotropic Zeeman splitting of ID holes formed on a (100) GaAs/AlGaAs heterostructure on a single cooldown. The strong spin-orbit coupling of holes and ID confinement gives rise to a highly anisotropic spin-splitting. In measuring quantum point contacts on the high symmetry (100) plane, we eliminate the effects of crystal anisotropy on our direct transport measurements of the Zeeman spin-splitting. We find that g^||_⊥QPC <; g^||_||QPC <; g^{⊥ (100)} where g^|| refers to the in-plane g-factors parallel and perpendicular to the QPC, and g^⊥(100) refers to the g-factor perpendicular to the 2D interface. We compare our data with existing theories and show that there are aspects of hole spin-splitting which remain to be understood.