  Renormalization of Landau level energies in graphene in strong magnetic field
due to Coulomb interaction is studied theoretically, and calculations are
compared with two experiments on carrier-density dependent scanning tunneling
spectroscopy. An approximate preservation of the square-root dependence of the
energies of Landau levels on their numbers and magnetic field in the presence
of the interaction is examined. Many-body calculations of the renormalized
Fermi velocity with the statically screened interaction taken in the
random-phase approximation show good agreement with both experiments. The
crucial role of the screening in achieving quantitative agreement is found. The
main contribution to the observed rapid logarithmic growth of the renormalized
Fermi velocity on approach to the charge neutrality point turned out to be
caused not by mere exchange interaction effects, but by weakening of the
screening at decreasing carrier density. The importance of a self-consistent
treatment of the screening is also demonstrated.
