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Nowadays it is experimentally feasible to create artificial, and inparticular, non-Abelian gauge potentials for ultracold atoms trapped in opticallattices. Motivated by this fact, we investigate the fundamental properties ofan ultracold Fermi gas in a non-Abelian U(2) gauge potential characterized by a\emph{constant} Wilson loop. Under this specific condition, the energy spectrumexhibits a robust band structure with large gaps and reveals a new fractalfigure. The transverse conductivity is related to topological invariants and isshown to be quantized when the Fermi energy lies inside a gap of the spectrum.We demonstrate that the analogue of the integer quantum Hall effect for neutralatoms survives the non-Abelian coupling and leads to a striking fractal phasediagram. Moreover, this coupling induces an anomalous Hall effect as observedin graphene.

Ultracold atomic gas in non-Abelian "magnetic" fields: the quantum Hall effect supremacy