Manifestation of a non-abelian gauge field in a p-type semiconductor system

Gauge theories, while describing fundamental interactions in nature, also emerge in a wide variety of physical systems. Abelian gauge fields have been predicted and observed in a number of novel quantum many-body systems, topological insulators, ultracold atoms and many others. However, the non-abelian gauge field, while playing the most fundamental role in particle physics, up to now has remained a purely theoretical construction in many-body physics. In the present paper we report the first observation of a non-abelian gauge field in a spin-orbit coupled quantum system. The gauge field manifests itself in quantum magnetic oscillations of a hole doped two-dimensional (2D) GaAs heterostructure. Transport measurements were performed in tilted magnetic fields, where the effect of the emergent non-abelian gauge field was controlled by the components of the magnetic field in the 2D plane.