Saddle point anomaly of Landau levels in graphenelike structures

Studying the tight binding model in an applied rational magnetic field (H) we show that graphene there are very unusual Landau levels situated immediate vicinity of saddle point (M-point) energy epsilon_M. around $\epsilon_M$ broadened into minibands (even relatively weak fields ~40-53 T) with maximal width reaching 0.4-0.5 separation between two neighboring though at all other energies is practically zero. In terms semiclassical approach a broad level or miniband epsilon_M manifestation so called self-intersecting orbit signifying abrupt transition from trajectories enclosing $\Gamma$ to K momentum space. Remarkably, virtually does not affect diamagnetic response graphene, which caused mostly by electron states Fermi \epsilon_F. Experimentally, effect broading can possibly be observed twisted where singularities brought close energy.