Magnetoelectronic properties of bilayer Bernal graphene

Abstract

The Peierls Hamiltonian band matrix is developed to investigate magnetoelectronic properties of bilayer Bernal graphene. A uniform perpendicular magnetic field creates 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. Two sets of effective quantum numbers, ${n}_{1}^{\mathit{eff}}$'s and ${n}_{2}^{\mathit{eff}}$'s, are required to characterize all the wave functions. They are determined by the strongest oscillation modes of the dominant carrier densities; furthermore, they rely on the specific interlayer atomic hoppings. The dependence of the quite low Landau-level energies on ${B}_{0}$ and ${n}_{1}^{\mathit{eff}}$ is approximately linear. An energy gap is produced by the magnetic field and interlayer atomic hoppings. ${E}_{g}$ grows with increasing field strength, while it is reduced by the Zeeman effect. The main features of magnetoelectronic structures are directly reflected in the density of states. The predicted electronic properties could be verified by the experimental measurements on absorption spectra and transport properties.