Landau level spectrum of bilayer Bernal graphene

Abstract

Landau level spectrum of bilayer Bernal graphene is investigated by using the Peierls Hamiltonian band matrix developed from the tight-binding model. A magnetic field leads a bilayer system to exhibit many dispersionless Landau levels(LLs) at low and high energies and some oscillatory LLs at moderate energy. State degeneracy of the low LLs is two times as much as that of the high LLs. Wave functions and state energies are dominated by the interlayer atomic interactions and field strength ( B 0). The former induce two groups of LLs, more low LLs, the asymmetric energy spectrum about the Fermi level, and the change of level spacing. The dependence of the pretty low Landau-level energies on the magnetic field and effective quantum number is approximately linear. An energy gap ( E g) is produced by the magnetic field and interlayer atomic hoppings. E g grows with the increasing field strength, while it is reduced due to the Zeeman effect. The predicted electronic properties could be verified by the measurements on magneto-optical and transport experiments.