Magnetoelectronic properties of normal and skewed phosphorene nanoribbons

The energy spectrum and eigenstates of single-layer black phosphorous nanoribbons in the presence of perpendicular magnetic field and in-plane transverse electric field are investigated by means of a tight-binding method and the effect of different types of edges is analytically examined. A description based on a new continuous model is proposed by expansion of the tight-binding model in the long-wavelength approximation. The wavefunctions corresponding to the flatband part of the spectrum are obtained analytically and are shown to approach agree well with the numerical results from the tight-binding method. Analytical expressions for the critical magnetic field at which Landau levels are formed and the ranges of wavenumbers in the dispersionless flat-band segments in the energy spectra are derived. We examine the evolution of the Landau levels when an in-plane lateral electric field is applied and determine analytically how the edge states shift with magnetic field.