Fermi velocity and effective mass of quasiparticles in bilayer phosphorene nanoribbons

Based on the Green’s function approach in combination with the tight-binding approximation, we have investigated the electronic properties of zigzag bilayer phosphorene nanoribbons (ZBLPNRs). A complete and fully reversible metal to semiconductor or insulator phase transition, has been observed via tuning a perpendicular electric field. We explain the effect of the interlayer hopping parameter on the electronic characterizations, namely, the energy band-gap, Fermi velocity and effective mass of carriers in biased ZBLPNRs. In the presence of the interlayer hopping term, the band structure of a ZBLPNR in the vicinity of the Fermi level has a form of two tilted Dirac cones, while, in the absence of it, the created cones are not tilted. Besides, the bands above and below the Fermi level are not symmetric,{\it i.e.}, there is no electron-hole symmetry for both limits of the interlayer coupling. A remarkable tuning of both the Fermi velocity and the reciprocal effective mass can be observed by adjusting the external bias voltage. At certain critical bias voltages, the band edge reciprocal masses and carrier velocities become zero, {\it i.e.}, the electrons exhibit a localization behaviour. This phenomenon indeed is a transition from massive to massless Dirac fermions and vice versa. The possibility of simultaneous control of the thermal and magnetic properties using an electric agent, which can be realized experimentally by using an perpendicular potential difference, open up possibilities for low power consumed thermomagnetic devices based on ZBLPNRs.