Tunable Electronic Properties of Multilayer Phosphorene and Its Nanoribbons

We study the effects of a vertical electric field on the electronic band structure and transport in multilayer phosphorene and its nanoribbons. In phosphorene, at a critical value of the vertical electric field ($E_c$), the band gap closes and the band structure undergoes a massive-to-massless Dirac fermion transition along the armchair direction. This transition is observable in quantum Hall measurements, as the power-law dependence of the Landau-level energy on the magnetic field $B$ goes from $\sim (n+1/2)B$ below $E_c$, to $\sim [(n+1/2)B]^{2/3}$ at $E_c$, to $\sim [(n+1/2)B]^{1/2}$ above $E_c$. In multilayer phosphorene nanoribbons (PNRs), the vertical electric field can be employed to manipulate the midgap energy bands that are associated with edge states, thereby giving rise to new device functionalities. We propose a dual-edge-gate PNR structure that works as a quantum switch.