dc and ac transport in few-layer black phosphorus

The multilayer band structure of black phosphorus (BP) is highly anisotropic, and its bandgap is tunable by applying a perpendicular electric field Ez . Within a linear response theory, we study dc and ac transport in few-layer BP, as functions of the Fermi energy, temperature, or frequency, in the presence of a Zeeman field. The current response to an in-plane electric field along two perpendicular directions is anisotropic and reflects that of the energy spectrum. In addition, we study the Hall conductivity and power absorption spectrum. The Hall conductivity vanishes, but the power spectrum P(ω) shows a considerable structure as a function of the normalized frequency α/hω=2Δ and/or of the bandgap 2Δ tuned by Ez. In particular, a clear maximum occurs in the difference between spin-up and spin-down contributions to P(ω). When potassium (K) atoms are deposited on top of BP, the anisotropy in the current response is stronger and the power spectrum is further modified. The results may be pertinent to the development of phosphorene-based applications