由於少層石墨能於實驗上的達成，它們在近年內吸引了很多的關注。除了可當成理想的二維材料，石墨的蜂巢狀結構也使得它具有獨特的電子性質。這些能帶結構會有效地受到層與層交互作用的影響，且會進一步受到外加磁場或電場的調制。在這工作中，我們利用Peierls tight-binding model來計算雙層石墨的磁電子能帶結構，同步考量了外加靜磁場及靜電場及層與層交互作用。外加場對於Landau level的能量及波函數是被仔細地討論。

　　雙層石墨在低頻是表現成兩對的拋物線能帶。而垂直磁場會將這二維的電子能態量子化成兩群的Landau levels。Landau state的簡併度會因外加電場的破壞；而分裂的能量差會隨著電場而增大。其中，能量最低的兩個Landau levels變化幅度最為明顯。Landau level的波函數可由4個次晶格所組成。波函數於次晶格間的分佈，會隨著電場及磁場大小而改變。

Few-layer graphenes have attracted a lot of attentions since they are achieved by recent experiments. Graphene is kind of ideal two-dimensional materials, and its honeycomb lattice results in the extraordinary electronic properties. The energy bands would be effectively influenced the interlayer interactions, and significantly modulated by external magnetic or electric fields. In this work, we employ the Peierls tight-binding model to evaluate the magneto-electronic structures of bilayer Bernal graphene. The magnetic and electric field, together with the interlayer interactions, are taken into account simultaneously. The field dependence of Landau energies and wave functions are investigated in detail.

　　The bilayer Bernal graphene possesses two pairs of parabolic bands in the low energy regions. And the perpendicular magnetic field substantially quantizes these energy bands into two groups of Landau levels. The degeneracy of these Landau states would be lifted by the external electric field, where the energy spacings split are broadened with field strength. The variation degree of the two lowest Landau levels is particularly evident. In addition, the wave function of Landau levels is governed by four sublattices. The way the wave function distributed over its subblattices would further vary with electric or magnetic fields.

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