  Nowadays it is experimentally feasible to create artificial, and in
particular, non-Abelian gauge potentials for ultracold atoms trapped in optical
lattices. Motivated by this fact, we investigate the fundamental properties of
an ultracold Fermi gas in a non-Abelian U(2) gauge potential characterized by a
\emph{constant} Wilson loop. Under this specific condition, the energy spectrum
exhibits a robust band structure with large gaps and reveals a new fractal
figure. The transverse conductivity is related to topological invariants and is
shown 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 neutral
atoms survives the non-Abelian coupling and leads to a striking fractal phase
diagram. Moreover, this coupling induces an anomalous Hall effect as observed
in graphene.
