Diverse magnetic quantization in bilayer silicene

The generalized tight-binding model is developed to investigate the rich and unique electronic properties of AB-bt bilayer silicene under the uniform perpendicular electric and magnetic fields. The first pair of conduction and valence bands, with an observable energy gap, possesses the unusual energy dispersions. Each group of conduction/valence Landau levels (LLs) is further classified into four subgroups; that is, there exist the sublattice- and spin-dominated LL subgroups. The magnetic-field-dependent LL energy spectra exhibit the irregular behavior corresponding to the critical points of band structure. Moreover, the electric field can create the frequent LL anti-crossings. The main features of LLs are revealed as many van Hove singularities in density of states. The feature-rich magnetic quantization directly reflects the geometric symmetries, the intralayer and interlayer atomic interactions, the spin-orbital couplings, and the field effects.