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

Hierarchy of Spin and Valley Symmetry Breaking in Quantum Hall Single Layer Graphene