  In a magnetic field bilayer graphene supports an octet of zero-energy Landau
levels with an extra twofold degeneracy in Landau orbitals n=0 and n=1. It is
shown that this orbital degeneracy is lifted due to Coulombic quantum
fluctuations of the valence band (the Dirac sea); this is a quantum effect
analogous to the Lamb shift in the hydrogen atom. A detailed study is made of
how these zero-energy levels evolve, with filling, into a variety of
pseudo-zero-mode Landau levels in the presence of possible spin and valley
breaking and Coulomb interactions, and a comparison is made with experimental
results.
