The generalized tight-binding model, based on the subenvelope functions of distinct sublattices, is developed to investigate the magnetic quantization in sliding bilayer graphenes. The relative shift of two graphene layers induces a dramatic transformation between the Dirac-cone structure and the parabolic band structure, and thus leads to drastic changes of Landau levels (LLs) in the spatial symmetry, initial formation energy, intergroup anti-crossing, state degeneracy and semiconductor-metal transition. There exist three kinds of LLs, i.e., well-behaved, perturbed and undefined LLs, which are characterized by a specific mode, a main mode plus side modes, and a disordered mode, respectively. Such LLs are clearly revealed in diverse magneto-optical selection rules. Specially, the undefined LLs frequently exhibit intergroup anti-crossings in the field-dependent energy spectra, and show a large number of absorption peaks without optical selection rules.

Electronic Coulomb excitations in monolayer silicene are investigated by using the Lindhard dielectric function and a newly developed generalized tight-binding model (G-TBM). G-TBM simultaneously contains the atomic interactions, the spin-orbit coupling, the Coulomb interactions, and the various external fields at an arbitrary chemical potential. We exhibit the calculation results of the electrically tunable magnetoplasmons and the strong magnetic field modulation of plasmon behaviors. The two intriguing phenomena are well explained by determining the dominant transition channels in the dielectric function and through understanding the electron behavior under the multiple interactions (intrinsic and external). A further tunability of the plasmon features is demonstrated with the momentum transfer and the Fermi energy. The methodological strategy could be extended to several other 2D materials like germanene and stanene, and might open a pathway to search a better system in nanoplasmonic applications.

We report an efficient technique to induce gatetunable two-dimensional superlattices in graphene by the combined action of a back gate and a few-layer graphene patterned bottom gate complementary to existing methods. The patterned gates in our approach can be easily fabricated and implemented in van der Waals stacking procedures, allowing flexible use of superlattices with arbitrary geometry. In transport measurements on a superlattice with a lattice constant a = 40 nm, wellpronounced satellite Dirac points and signatures of the Hofstadter butterfly including a nonmonotonic quantum Hall response are observed. Furthermore, the experimental results are accurately reproduced in transport simulations and show good agreement with features in the calculated band structure. Overall, we present a comprehensive picture of graphene-based superlattices, featuring a broad range of miniband effects, both in experiment and in theoretical modeling. The presented technique is suitable for studying more advanced geometries which are not accessible by other methods.

Electronic properties of few-layer phosphorenes are investigated by the generalized tight-binding model. They are greatly diversified by the electric and magnetic fields (E z and B z ). The E z -induced gap transition, Dirac cones, oscillatory bands and critical points are present in bilayer system, but absent in monolayer one. The diverse magnetic quantization phenomena cover the coexistent two subgroups of Landau levels, the uniform and non-uniform energy spacings, and the crossing and anti-crossing behaviors. Specifically, the wavefunctions exhibit the dramatic changes between the well-behaved and multi-mode oscillations. The feature-rich energy spectra are reveled in density of states as .many special structures which could be verified from scanning tunneling spectroscopy.

We consider graphene superlattice miniband fermions probed by electronic interferometry in magnetotransport experiments. By decoding the observed Fabry-Pérot interference patterns together with our corresponding quantum transport simulations, we find that the Dirac quasiparticles originating from the superlattice minibands do not undergo conventional cyclotron motion but follow more subtle trajectories. In particular, dynamics at low magnetic fields is characterized by peculiar, straight trajectory segments. Our results provide new insights into superlattice miniband fermions and open up novel possibilities to use periodic potentials in electron optics experiments.