Magnetic field driven instability of charged center in graphene
  It is shown that a magnetic field dramatically affects the problem of supercritical charge in graphene making any charge in gapless theory supercritical. The cases of radially symmetric potential well and Coulomb center in an homogeneous magnetic field are considered. The local density of states and polarization charge density are calculated in the first order of perturbation theory. It is argued that the magnetically induced instability of the supercritical Coulomb center can be considered as a quantum mechanical counterpart of the magnetic catalysis phenomenon in graphene. 
O. V. Gamayun, E. V. Gorbar, and V. P. Gusynin
cond-mat.str-el