Dirac Electrons in a Planar Potential Well in a Magnetic Field - Gamayun, O.V.; Gorbar, E.V.; Gusynin, V.P. (Ukrainian Journal of Physics, 2022)
We study the Dirac equation in two spatial dimensions for quasiparticles in a potential well in graphene in a homogeneous magnetic field. It is shown that, at some critical value of the potential strength, the lowest empty energy level crosses a filled negative energy level leading to the instability of the system. The critical potential strength decreases with decrease of a quasiparticle gap and becomes zero in the gapless case. It is argued that the magnetically driven instability of a charged center can be considered as a quantum mechanical counterpart of the magnetic catalysis phenomenon in graphene.