Field-created diverse quantizations in phosphorenes

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.