Energy spectra of ABC-stacked trilayer graphene in magnetic and electric fields

We have developed the generalized tight-binding model to understand how the electronic structures of ABC-stacked trilayer graphene can be modulated by external fields. A band-like Hamiltonian matrix is used to obtain the electronic properties efficiently. A uniform perpendicular magnetic field gives rise to three groups of Landau levels that can be distinguished from one another by the subenvelope functions of the distinct sublattices. Intergroup Landau-level anticrossings occurring between any two groups and intragroup anticrossings coming from the second group are revealed in the magnetic field-dependent energy spectrum. Such anticrossings are induced by specific interlayer atomic interactions. In the presence of an electric field, each Landau-level group will split into two subgroups, which are characterized by the two different localization centers. The anticrossings in the second group can be suppressed or produced by varying the electric field strength, the reason being the significant modification of the band structures. Furthermore, the intragroup anticrossings arise in two split subgroups of the first group.