Diverse Magnetic Quantization in Bilayer Silicene

The generalized tight-binding model is developed to investigate the rich and unique electronic properties of AB-bt (bottom-top) bilayer silicene under uniform perpendicular electric and magnetic fields. The first pair of conduction and valence bands, with an observable energy gap, displays 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 irregular behavior corresponding to the critical points of the band structure. Moreover, the electric field can induce many LL anti-crossings. The main features of the LLs are uncovered with many van Hove singularities in the density-of-states and non-uniform delta-function-like peaks in the magneto-absorption spectra. The feature-rich magnetic quantization directly reflects the geometric symmetries, intra-layer and inter-layer atomic interactions, spin-orbital couplings, and the field effects. The results of this work can be applied to novel designs of $Si$-based nano-electronics and nano-devices with enhanced mobilities.