  We explore several microscopic mechanisms for breaking the $n=0$ fourfold
Landau level degeneracy in a single-layer graphene. Valley-scattering random
potential, Zeeman interaction, and electron-phonon coupling are considered in
the presence of SU(4)-symmetric Coulomb exchange interaction. Among all the
mechanisms considered, it is the electron-phonon coupling combined with the
Zeeman interaction which leads to the full splitting of the $n=0$ Landau
levels. A recent controversy of "valley-first" or "spin-first" breaking of
SU(4) symmetry of the $n=0$ graphene Landau level is examined in light of our
results. Existence of midgap states between Landau levels of opposite valley
polarity are demonstrated.
